Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #30412 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#32692 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G | |
610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,18)(14,15,19,17)(21,24)(22,26)(28,29,32,34)(30,33,38,41)(31,35,39,43)(36,40,37,42);(12,14,16,19)(13,17,18,15)(20,21,23,24)(22,25,26,27)(28,30,32,38)(29,33,34,41)(31,36,39,37)(35,40,43,42);(20,22,23,26)(21,25,24,27)(30,36)(31,39)(33,40)(35,43)(37,38)(41,42);(12,15,16,17)(13,14,18,19)(21,24)(25,27)(29,34)(33,41)(35,43)(40,42)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 25680);