Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23872 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23875 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1642 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)(14,24)(15,20)(16,29)(17,32)(18,23)(19,26)(21,30)(22,34)(25,35)(27,43)(28,36)(31,39)(33,38)(37,42)(40,41);(12,14,18,15)(13,19,23,36)(16,25,31,27)(17,28,34,26)(20,32,24,22)(21,35,38,43)(29,40,39,37)(30,42,33,41);(12,15,18,14)(13,20,23,24)(16,27,31,25)(17,26,34,28)(19,22,36,32)(21,37,38,40)(29,35,39,43)(30,41,33,42);(12,16)(13,21)(14,25)(15,27)(17,33)(18,31)(19,35)(20,37)(22,39)(23,38)(24,40)(26,42)(28,41)(29,32)(30,34)(36,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16863);