Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13334 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13334 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2011 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G | |
568 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,25)(15,19)(16,32)(17,35)(18,23)(20,26)(21,29)(22,33)(24,31)(27,40)(28,37)(30,39)(34,42)(36,41)(38,43);(13,19)(15,29)(16,33)(17,31)(20,25)(21,24)(22,35)(23,32)(26,34)(27,36)(30,43)(37,38)(39,40)(41,42);(12,14)(13,20)(15,30)(16,34)(17,36)(18,28)(19,37)(21,40)(22,41)(23,38)(24,42)(25,32)(26,33)(27,31)(29,43)(35,39)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6322);