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×#32895 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
3540 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)(13,19)(14,23)(16,17)(21,36)(22,28)(24,38)(25,30)(26,29)(31,34)(32,37)(33,42)(39,40);(12,13)(14,20)(15,21)(16,28)(17,19)(18,22)(23,34)(24,33)(25,35)(26,32)(27,37)(29,36)(30,31)(38,43)(39,41)(40,42);(12,14,18,25)(13,20,22,35)(15,24,27,40)(16,23,17,30)(19,31,28,34)(21,33,37,42)(26,39,29,38)(32,41,36,43);(12,15)(13,21)(14,24)(16,29)(17,26)(18,27)(19,32)(20,33)(22,37)(23,38)(25,40)(28,36)(30,39)(31,41)(34,43)(35,42)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 25883);