Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18284 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18298 |
| 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 | |
1024 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)(13,20)(14,25)(15,30)(16,26)(21,39)(22,41)(23,32)(24,38)(27,31)(28,29)(33,34)(35,43)(36,37)(40,42);(12,13)(14,21)(15,22)(16,32)(17,35)(18,23)(19,24)(20,26)(25,41)(27,42)(28,37)(29,40)(30,36)(31,39)(33,38)(34,43);(12,14,19,29)(13,21,24,40)(15,26,30,33)(16,31,34,27)(17,25,18,28)(20,36,38,22)(23,37,35,41)(32,39,43,42);(12,15,18,27)(13,22,23,42)(14,26,28,16)(17,31,19,30)(20,37,32,21)(24,36,35,39)(25,34,29,33)(38,41,43,40)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11286);