#!/usr/bin/perl
use strict;
use warnings;

{
    local $/ = '>Group';
    while (<DATA>) {
        chomp;
        print ">Group$_" if tr/\n// > 2;
    }   
}


__DATA__
>Group 42
0    25ap, >name_06-T_1_0... at 92.00%
1    28ap, >name_06-T_1_0... *
>Group 43
0    28ap, >name_07-N_1_0... *
>Group 44
0    29ap, >name_07-N_1_0... *
>Group 45
0    25ap, >name_03-T_1_0... *
1    25ap, >name_06-T_1_0... at 100.00%
2    25ap, >name_07-N_1_0... at 100.00%
3    25ap, >name_11-N_1_0... at 100.00%
4    25ap, >name_14-T_1_0... at 100.00%
[download]

prints

>Group 42
0       25ap, >name_06-T_1_0... at 92.00%
1       28ap, >name_06-T_1_0... *
>Group 45
0       25ap, >name_03-T_1_0... *
1       25ap, >name_06-T_1_0... at 100.00%
2       25ap, >name_07-N_1_0... at 100.00%
3       25ap, >name_11-N_1_0... at 100.00%
4       25ap, >name_14-T_1_0... at 100.00%
[download]

If you want to separate the records with a newline in the output, add a newline in the print. print ">Group$_\n" if tr/\n// > 2;