Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18416 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
978 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)(13,18)(14,22)(15,25)(19,31)(20,29)(21,26)(23,35)(24,38)(27,40)(30,33)(32,42)(34,41)(36,37)(39,43);(12,13,16,21)(14,19,23,32)(15,26,25,18)(17,20,28,34)(22,33,35,43)(24,39,37,30)(27,41,40,29)(31,36,42,38);(14,23)(15,27)(18,29)(19,32)(22,35)(24,38)(25,40)(26,41)(30,42)(31,39)(33,43)(36,37);(12,14)(13,19)(15,24)(16,23)(17,22)(18,30)(20,33)(21,32)(25,37)(26,39)(27,36)(28,35)(29,31)(34,43)(38,40)(41,42)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11404);