Finite Group DatabasebetaFinite Group DatabasebetaGroups equal to their own commutator subgroup (G' = G).
| order | group | # | quasisimple | simple | superperfect |
|---|---|---|---|---|---|
| 60 | A5 #304 | ✓ | ✓ | – | |
| 120 | SL(2,𝔽5) #1195 | ✓ | – | ✓ | |
| 168 | GL(3,𝔽2) #4272 | ✓ | ✓ | – | |
| 336 | SL(2,𝔽7) #66645 | ✓ | – | ✓ | |
| 360 | A6 #67188 | ✓ | ✓ | – | |
| 504 | SL(2,𝔽8) #92730 | ✓ | ✓ | ✓ | |
| 660 | PSL(2,𝔽11) #10620343 | ✓ | ✓ | – | |
| 720 | SL(2,𝔽9) #10623940 | ✓ | – | – | |
| 960 | #11757162 | #1 | – | – | – |
| 960 | #11757163 | #2 | – | – | – |
| 1080 | #11761914 | ✓ | – | – | |
| 1092 | PSL(2,𝔽13) #11763977 | ✓ | ✓ | – | |
| 1320 | SL(2,𝔽11) #13050309 | ✓ | – | ✓ | |
| 1344 | AGL(3,𝔽2) #13062397 | #1 | – | – | – |
| 1344 | #13051525 | #2 | – | – | – |
| 1920 | #14515300 | #1 | – | – | – |
| 1920 | #14515301 | #2 | – | – | – |
| 1920 | #14515302 | #3 | – | – | – |
| 1920 | #14515303 | #4 | – | – | – |
| 1920 | #14515304 | #5 | – | – | – |
| 1920 | #14515305 | #6 | – | – | – |
| 1920 | 2−1+4⋊A5 #14515306 | #7 | – | – | – |
| 2160 | #72209591 | ✓ | – | ✓ | |
| 2184 | Sp(2,𝔽13) #72209592 | ✓ | – | ✓ | |
| 2448 | PSL(2,𝔽17) #72209593 | ✓ | ✓ | – | |
| 2520 | A7 #72209594 | ✓ | ✓ | – | |
| 2688 | #72209595 | #1 | – | – | – |
| 2688 | #72209596 | #2 | – | – | – |
| 2688 | #72209597 | #3 | – | – | ✓ |
| 3000 | #72209598 | – | – | – | |
| 3420 | PSL(2,𝔽19) #16811951 | ✓ | ✓ | – | |
| 3600 | A52 #72209599 | – | – | – | |
| 3840 | #72209600 | #1 | – | – | – |
| 3840 | #72209601 | #2 | – | – | – |
| 3840 | #72209602 | #3 | – | – | – |
| 3840 | #72209603 | #4 | – | – | – |
| 3840 | #72209604 | #5 | – | – | – |
| 3840 | #72209605 | #6 | – | – | ✓ |
| 3840 | #72209606 | #7 | – | – | ✓ |
| 4080 | SL(2,𝔽16) #72209607 | ✓ | ✓ | ✓ | |
| 4860 | #72209608 | #1 | – | – | – |
| 4860 | #72209609 | #2 | – | – | – |
| 4896 | Sp(2,𝔽17) #72209610 | ✓ | – | ✓ | |
| 5040 | #72209611 | ✓ | – | – | |
| 5376 | #72209612 | – | – | ✓ | |
| 5616 | SL(3,𝔽3) #72209613 | ✓ | ✓ | ✓ | |
| 5760 | #72209614 | – | – | – | |
| 6048 | SU(3,𝔽3) #72209615 | ✓ | ✓ | ✓ | |
| 6072 | PSL(2,𝔽23) #72209616 | ✓ | ✓ | – | |
| 6840 | Sp(2,𝔽19) #72209617 | ✓ | – | ✓ | |
| 7200 | A5×SL(2,𝔽5) #72209618 | #1 | – | – | – |
| 7200 | Ω+(4,𝔽5) #72209619 | #2 | – | – | – |
| 7500 | #72209620 | #1 | – | – | – |
| 7500 | #72209621 | #2 | – | – | – |
| 7560 | #72209622 | ✓ | – | – | |
| 7680 | #72209624 | #1 | – | – | – |
| 7680 | #72209626 | #2 | – | – | – |
| 7680 | #72209628 | #3 | – | – | – |
| 7680 | #72209630 | #4 | – | – | – |
| 7680 | #72209632 | #5 | – | – | – |
| 7800 | PSL(2,𝔽25) #72209633 | ✓ | ✓ | – | |
| 7920 | M11 #72209634 | ✓ | ✓ | ✓ | |
| 9720 | #72209635 | #1 | – | – | – |
| 9720 | #72209636 | #2 | – | – | ✓ |
| 9720 | #72209637 | #3 | – | – | – |
| 9828 | PSL(2,𝔽27) #72209638 | ✓ | ✓ | – | |
| 10080 | A5×GL(3,𝔽2) #72209640 | – | – | – | |
| 10752 | #72209643 | #1 | – | – | – |
| 10752 | #72209646 | #2 | – | – | – |
| 10752 | #72209649 | #3 | – | – | – |
| 10752 | #72209652 | #4 | – | – | – |
| 10752 | #72209654 | #5 | – | – | – |
| 10752 | #72209657 | #6 | – | – | – |
| 10752 | #72209659 | #7 | – | – | – |
| 10752 | #72209662 | #8 | – | – | – |
| 10752 | #72209665 | #9 | – | – | – |
| 11520 | #72209666 | #1 | – | – | – |
| 11520 | #72209667 | #2 | – | – | – |
| 11520 | #72209668 | #3 | – | – | – |
| 11520 | #72209669 | #4 | – | – | – |
| 12144 | Sp(2,𝔽23) #72209670 | ✓ | – | ✓ | |
| 12180 | PSL(2,𝔽29) #27131832 | ✓ | ✓ | – | |
| 14400 | SL(2,𝔽5)2 #72209673 | – | – | ✓ | |
| 14520 | #72209675 | – | – | – | |
| 14580 | #72209678 | – | – | – | |
| 14880 | PSL(2,𝔽31) #72209679 | ✓ | ✓ | – | |
| 15000 | #72209682 | #1 | – | – | – |
| 15000 | SL(2,ℤ/25) #72209684 | #2 | – | – | ✓ |
| 15000 | #72209687 | #3 | – | – | ✓ |
| 15120 | #72209688 | ✓ | – | ✓ | |
| 15360 | #72209693 | #1 | – | – | – |
| 15360 | #72209698 | #2 | – | – | – |
| 15360 | #72209703 | #3 | – | – | – |
| 15360 | #72209709 | #4 | – | – | – |
| 15360 | #72209715 | #5 | – | – | – |
| 15360 | #72209721 | #6 | – | – | – |
| 15360 | #72209728 | #7 | – | – | – |
| 15600 | SL(2,𝔽25) #72209729 | ✓ | – | ✓ | |
| 16464 | #72209732 | – | – | – | |
| 17280 | #72209735 | – | – | – |