Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of D64 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#7537 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | D32 |
| commutator | C32 | C2×C4×C11 |
| Frattini, cosocle | C2×C32 | C22×C11 |
| prime radical | C2×C11×D32 | C2 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C4×C11 ◁ C2×C8×C11 ◁ C2×C11×C16 ◁ C2×C11×C32 ◁ G | |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 2 generators on 79 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(16,17)(18,23)(19,34)(20,38)(21,41)(22,28)(24,29)(25,30)(26,35)(27,39)(31,51)(32,53)(33,45)(36,69)(37,67)(40,71)(42,55)(43,54)(44,62)(46,61)(47,64)(48,57)(49,70)(50,60)(52,68)(56,72)(58,66)(59,65)(63,76)(73,79)(74,78)(75,77);(17,23)(18,29)(19,30)(20,35)(21,39)(24,25)(26,51)(27,53)(28,45)(31,61)(32,64)(33,57)(34,42)(36,70)(37,60)(38,43)(40,68)(41,44)(46,66)(47,65)(48,50)(49,72)(52,76)(54,55)(56,62)(58,59)(63,79)(67,74)(69,73)(71,75)(77,78)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 525);