Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23995 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#23995 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #535 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | #2404 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G | |
1164 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)(14,18)(15,19)(16,21)(17,22)(20,24)(23,34)(25,32)(26,43)(27,35)(28,36)(29,38)(30,39)(31,40)(33,42)(37,41);(12,14)(13,18)(15,26,27,42)(16,25)(17,24)(19,33,35,43)(20,22)(21,32)(23,28,40,29)(30,41)(31,36,34,38)(37,39);(12,15)(13,19)(14,23)(16,29)(17,27)(18,31)(20,34)(21,38)(22,35)(24,40)(25,42)(26,41)(28,30)(32,43)(33,37)(36,39);(12,14)(13,20)(15,23)(16,25)(17,24)(18,22)(19,34)(21,37)(26,28)(27,40)(29,42)(30,41)(31,35)(32,39)(33,38)(36,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16983);