Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#23787 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C11×#376 ◁ G | |
712 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21,23,25)(22,26,27,24)(28,29)(30,36)(31,34)(32,35)(33,38)(37,42)(39,41)(40,43);(13,16)(17,19)(28,30)(29,33)(31,38)(32,37)(34,36)(35,41)(39,40)(42,43);(20,22,23,27)(21,24,25,26)(30,37)(32,40)(33,41)(35,43)(36,42)(38,39);(12,14,15,18)(13,17,16,19)(29,34)(33,36)(35,43)(41,42)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16775);