Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23998 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#23999 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1146 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)(14,22)(15,19)(16,29)(17,21)(18,26)(20,32)(23,30)(24,40)(25,36)(27,37)(28,35)(31,34)(33,42)(38,41)(39,43);(12,13)(14,23,25,18)(15,19)(16,20)(17,21)(22,26,36,30)(24,39,41,33)(27,34)(28,35)(29,32)(31,37)(38,43,40,42);(12,14)(13,18)(15,24)(16,30)(17,25)(19,33)(20,36)(21,23)(22,29)(26,32)(27,43)(28,41)(31,42)(34,38)(35,39)(37,40);(12,15,17,28)(13,19,21,35)(14,24,25,41)(16,31,32,27)(18,33,23,39)(20,37,29,34)(22,38,36,40)(26,43,30,42)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16987);