Finite Group DatabasebetaFinite Group Databasebeta| order | 3840 |
| isoclinism | isoclinic class of #72209603 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C22 | #11757162 |
| commutator, hypocenter | G | C1 |
| Fitting, cosocle | C26 | A5 |
| LCS | G | |
| UCS | C1 ◁ C22 | |
411 conjugacy classes of subgroups; only the 7 normal subgroups are shown.
This group has 411 conjugacy classes of subgroups — too many to draw. Only its 7 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)(4,11,10,12)(6,8,7,9)(13,18,14,17)(15,21,19,22)(16,25,20,26)(23,30,24,31)(27,33,28,34)(29,35,32,36)(37,42,38,41)(39,44,43,40)(45,48,46,47);(1,4,2)(3,5,10)(6,13,8)(7,14,9)(11,15,16)(12,19,20)(17,23,28)(18,24,27)(21,26,29)(22,25,32)(30,33,37)(31,34,38)(35,39,40)(36,43,44)(41,45,47)(42,46,48);(1,5)(2,8)(3,9)(4,13)(6,7)(10,14)(11,17)(12,18)(15,23)(16,20)(19,24)(21,30)(22,31)(25,26)(27,28)(29,37)(32,38)(33,34)(35,41)(36,42)(39,45)(40,44)(43,46)(47,48);(1,6)(2,9)(3,8)(4,14)(5,7)(10,13)(11,12)(15,19)(16,27)(17,18)(20,28)(21,22)(23,24)(25,33)(26,34)(29,32)(30,31)(35,42)(36,41)(37,38)(39,46)(40,47)(43,45)(44,48);(1,6)(2,3)(4,14)(5,7)(8,9)(10,13)(11,18)(12,17)(15,23)(16,20)(19,24)(21,30)(22,31)(25,26)(27,28)(29,38)(32,37)(33,34)(35,42)(36,41)(39,43)(40,47)(44,48)(45,46);(1,7)(2,8)(3,9)(4,10)(5,6)(11,17)(12,18)(13,14)(15,19)(16,27)(20,28)(21,22)(23,24)(25,33)(26,34)(29,37)(30,31)(32,38)(35,36)(39,45)(40,48)(41,42)(43,46)(44,47);(1,5)(2,3)(4,10)(6,7)(8,9)(11,12)(13,14)(15,19)(16,20)(17,18)(21,22)(23,24)(25,26)(27,28)(29,32)(30,31)(33,34)(35,36)(37,38)(39,43)(40,44)(41,42)(45,46)(47,48);(1,6)(2,8)(3,9)(4,13)(5,7)(10,14)(11,18)(12,17)(15,24)(16,27)(19,23)(20,28)(21,31)(22,30)(25,33)(26,34)(29,38)(32,37)(35,41)(36,42)(39,45)(40,47)(43,46)(44,48)30 conjugacy classes — view the full character table.
| maximal subgroup of | #72249859, #72257142, #72257356, … |
| maximal quotient of | #72209626, #72209628, #72209632, … |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((1,2,5,3)(4,11,10,12)(6,8,7,9)(13,18,14,17)(15,21,19,22)(16,25,20,26)(23,30,24,31)(27,33,28,34)(29,35,32,36)(37,42,38,41)(39,44,43,40)(45,48,46,47), (1,4,2)(3,5,10)(6,13,8)(7,14,9)(11,15,16)(12,19,20)(17,23,28)(18,24,27)(21,26,29)(22,25,32)(30,33,37)(31,34,38)(35,39,40)(36,43,44)(41,45,47)(42,46,48), (1,5)(2,8)(3,9)(4,13)(6,7)(10,14)(11,17)(12,18)(15,23)(16,20)(19,24)(21,30)(22,31)(25,26)(27,28)(29,37)(32,38)(33,34)(35,41)(36,42)(39,45)(40,44)(43,46)(47,48), (1,6)(2,9)(3,8)(4,14)(5,7)(10,13)(11,12)(15,19)(16,27)(17,18)(20,28)(21,22)(23,24)(25,33)(26,34)(29,32)(30,31)(35,42)(36,41)(37,38)(39,46)(40,47)(43,45)(44,48), (1,6)(2,3)(4,14)(5,7)(8,9)(10,13)(11,18)(12,17)(15,23)(16,20)(19,24)(21,30)(22,31)(25,26)(27,28)(29,38)(32,37)(33,34)(35,42)(36,41)(39,43)(40,47)(44,48)(45,46), (1,7)(2,8)(3,9)(4,10)(5,6)(11,17)(12,18)(13,14)(15,19)(16,27)(20,28)(21,22)(23,24)(25,33)(26,34)(29,37)(30,31)(32,38)(35,36)(39,45)(40,48)(41,42)(43,46)(44,47), (1,5)(2,3)(4,10)(6,7)(8,9)(11,12)(13,14)(15,19)(16,20)(17,18)(21,22)(23,24)(25,26)(27,28)(29,32)(30,31)(33,34)(35,36)(37,38)(39,43)(40,44)(41,42)(45,46)(47,48), (1,6)(2,8)(3,9)(4,13)(5,7)(10,14)(11,18)(12,17)(15,24)(16,27)(19,23)(20,28)(21,31)(22,30)(25,33)(26,34)(29,38)(32,37)(35,41)(36,42)(39,45)(40,47)(43,46)(44,48));