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×#32896 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×H(7,𝔽2) | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
3610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,18,24)(14,25,28,38)(15,21,30,37)(16,23,17,22)(19,31,35,27)(20,32,36,29)(26,33,43,40)(34,42,39,41);(12,14)(13,19)(15,26)(16,31)(17,27)(18,28)(20,33)(21,34)(22,38)(23,25)(24,35)(29,42)(30,43)(32,41)(36,40)(37,39);(12,15)(13,20)(14,26)(16,29)(17,32)(18,30)(19,33)(21,22)(23,37)(24,36)(25,39)(27,41)(28,43)(31,42)(34,38)(35,40);(12,15)(13,21)(14,26)(16,32)(17,29)(18,30)(19,34)(20,22)(23,36)(24,37)(25,40)(27,42)(28,43)(31,41)(33,38)(35,39)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 25884);