Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61106 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61108 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
2592 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 75 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,26)(15,31)(16,22)(17,25)(18,24)(19,23)(20,29)(21,33)(27,41)(28,53)(30,49)(32,61)(34,51)(35,66)(36,50)(37,47)(38,43)(39,48)(40,45)(42,58)(44,64)(46,59)(52,56)(54,67)(55,60)(57,68)(62,72)(63,70)(65,71)(69,74)(73,75);(12,14)(13,20)(15,27)(16,35)(17,38)(18,29)(19,30)(21,41)(22,46)(23,43)(24,49)(25,26)(28,36)(31,60)(32,62)(33,56)(34,57)(37,58)(39,59)(40,55)(42,48)(44,69)(45,68)(47,53)(50,66)(51,52)(54,63)(61,75)(64,73)(65,74)(67,71)(70,72);(12,15,19,34)(13,21,23,45)(14,27,30,57)(16,32,37,65)(17,33,18,40)(20,41,43,68)(22,44,47,70)(24,31,25,51)(26,52,49,60)(28,54,59,73)(29,55,38,56)(35,62,58,74)(36,63,39,64)(42,67,66,75)(46,69,53,72)(48,71,50,61);(12,16)(13,22)(14,28)(15,32)(17,39)(18,36)(19,37)(20,42)(21,44)(23,47)(24,50)(25,48)(26,53)(27,54)(29,58)(30,59)(31,61)(33,64)(34,65)(35,38)(40,63)(41,67)(43,66)(45,70)(46,49)(51,71)(52,72)(55,74)(56,62)(57,73)(60,69)(68,75);(13,23)(20,43)(21,45)(22,47)(24,25)(26,49)(31,51)(41,68)(42,66)(44,70)(46,53)(48,50)(52,60)(61,71)(67,75)(69,72)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54096);