Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #31077 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#32703 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | H(3,𝔽4) |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | #2782 |
| prime radical | C11×#575 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G | |
476 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)(12,13,17,21,18,23,16,22)(14,24,27,19,28,35,26,36)(15,29,33,20,31,39,32,38)(25,40,41,37,42,34,30,43);(12,14)(13,19)(15,30)(16,26)(17,27)(18,28)(20,37)(21,35)(22,24)(23,36)(25,33)(29,40)(31,41)(32,42)(34,39)(38,43);(12,15,16,32,18,31,17,33)(13,20,21,39,23,38,22,29)(14,25,27,41,28,42,26,30)(19,34,24,37,36,40,35,43);(14,26,28,27)(15,31)(19,35,36,24)(20,38)(25,41,42,30)(29,39)(32,33)(34,37,40,43)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 25691);