Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18132 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18138 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C25×C11 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1054 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)(14,22,24,38)(15,26,28,40)(16,19,30,34)(18,31,33,23)(20,35,37,29)(25,36,39,43)(27,32,41,42);(12,14,16,25)(13,18,19,32)(15,27,29,23)(17,24,30,39)(20,36,26,22)(21,33,34,42)(28,41,35,31)(37,43,40,38);(15,28)(20,37)(22,38)(23,31)(26,40)(27,41)(29,35)(36,43);(13,19)(18,32)(20,26)(21,34)(22,36)(33,42)(37,40)(38,43)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11126);