Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24295 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24297 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2408 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1334 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)(12,13,19,22)(14,17,25,18)(15,26,30,23)(16,24,33,38)(20,28,35,29)(21,32,36,31)(27,34,42,43)(37,40,39,41);(12,14,17,22,19,25,18,13)(15,20,28,23,30,35,29,26)(16,24,31,36,33,38,32,21)(27,34,40,37,42,43,41,39);(12,15)(13,20)(14,23)(16,27)(17,28)(18,29)(19,30)(21,34)(22,35)(24,37)(25,26)(31,40)(32,41)(33,42)(36,43)(38,39);(12,16,18,32,19,33,17,31)(13,21,25,38,22,36,14,24)(15,27,29,41,30,42,28,40)(20,34,26,39,35,43,23,37)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17285);