Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32894 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#32897 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×2−1+6 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
3512 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 75 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,19,25)(14,26,30,47)(15,31,34,49)(16,22,36,46)(17,24,18,23)(20,37,42,29)(21,39,44,33)(27,40,55,66)(28,56,59,51)(32,61,64,68)(35,48,38,45)(41,58,67,57)(43,62,69,63)(50,53,60,54)(52,71,73,65)(70,72,75,74);(12,14)(13,20)(15,27)(16,28)(17,37)(18,29)(19,30)(21,40)(22,41)(23,47)(24,26)(25,42)(31,60)(32,52)(33,54)(34,55)(35,58)(36,59)(38,57)(39,53)(43,65)(44,66)(45,51)(46,67)(48,56)(49,50)(61,75)(62,74)(63,72)(64,73)(68,70)(69,71);(12,15,19,34)(13,21,25,44)(14,27,30,55)(16,32,36,64)(17,33,18,39)(20,40,42,66)(22,43,46,69)(23,31,24,49)(26,50,47,60)(28,52,59,73)(29,53,37,54)(35,62,38,63)(41,65,67,71)(45,68,48,61)(51,70,56,75)(57,72,58,74);(12,16)(13,22)(14,28)(15,32)(17,38)(18,35)(19,36)(20,41)(21,43)(23,48)(24,45)(25,46)(26,51)(27,52)(29,58)(30,59)(31,61)(33,63)(34,64)(37,57)(39,62)(40,65)(42,67)(44,69)(47,56)(49,68)(50,70)(53,74)(54,72)(55,73)(60,75)(66,71)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 25885);