Finite Group DatabasebetaFinite Group Databasebeta| order | 7680 |
| isoclinism | isoclinic class of #72209632 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C22 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C23 | #11757162 |
| commutator, hypocenter | G | C1 |
| Fitting, cosocle | C27 | A5 |
| LCS | G | |
| UCS | C1 ◁ C23 | |
2269 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 2269 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Permutation generators:
(1,2,5,3)(4,7,6,8)(9,13,11,14)(10,15,12,16)(17,19,18,20)(21,24,23,22)(25,26)(27,34)(28,33)(29,31)(30,32)(35,42)(36,40)(37,41);(1,4,2)(3,5,6)(7,9,10)(8,11,12)(13,16,17)(14,15,18)(19,21,22)(20,23,24)(25,27,26)(28,37,33)(29,35,31)(30,36,32)(34,38,39)(40,43,48)(41,44,46)(42,45,47);(1,5)(2,3)(4,6)(7,8)(9,11)(10,12)(13,14)(15,16)(17,18)(19,20)(21,23)(22,24);(25,28)(26,31)(27,35)(29,30)(32,33)(34,40)(36,37)(38,43)(39,46)(41,42)(44,45)(47,48);(25,29)(26,32)(27,36)(28,30)(31,33)(34,41)(35,37)(38,44)(39,47)(40,42)(43,45)(46,48);(25,29)(26,33)(27,36)(28,30)(31,32)(34,42)(35,37)(38,43)(39,46)(40,41)(44,45)(47,48);(25,30)(26,31)(27,37)(28,29)(32,33)(34,40)(35,36)(38,44)(39,47)(41,42)(43,45)(46,48);(25,29)(26,31)(27,35)(28,30)(32,33)(34,42)(36,37)(38,45)(39,47)(40,41)(43,44)(46,48);(25,28)(26,33)(27,37)(29,30)(31,32)(34,41)(35,36)(38,44)(39,46)(40,42)(43,45)(47,48)56 conjugacy classes — view the full character table.
| maximal quotient of | #72209698 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((1,2,5,3)(4,7,6,8)(9,13,11,14)(10,15,12,16)(17,19,18,20)(21,24,23,22)(25,26)(27,34)(28,33)(29,31)(30,32)(35,42)(36,40)(37,41), (1,4,2)(3,5,6)(7,9,10)(8,11,12)(13,16,17)(14,15,18)(19,21,22)(20,23,24)(25,27,26)(28,37,33)(29,35,31)(30,36,32)(34,38,39)(40,43,48)(41,44,46)(42,45,47), (1,5)(2,3)(4,6)(7,8)(9,11)(10,12)(13,14)(15,16)(17,18)(19,20)(21,23)(22,24), (25,28)(26,31)(27,35)(29,30)(32,33)(34,40)(36,37)(38,43)(39,46)(41,42)(44,45)(47,48), (25,29)(26,32)(27,36)(28,30)(31,33)(34,41)(35,37)(38,44)(39,47)(40,42)(43,45)(46,48), (25,29)(26,33)(27,36)(28,30)(31,32)(34,42)(35,37)(38,43)(39,46)(40,41)(44,45)(47,48), (25,30)(26,31)(27,37)(28,29)(32,33)(34,40)(35,36)(38,44)(39,47)(41,42)(43,45)(46,48), (25,29)(26,31)(27,35)(28,30)(32,33)(34,42)(36,37)(38,45)(39,47)(40,41)(43,44)(46,48), (25,28)(26,33)(27,37)(29,30)(31,32)(34,41)(35,36)(38,44)(39,46)(40,42)(43,45)(47,48));