Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3198 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#17989 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C42 | C24×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C11×#3169 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C11×#431 ◁ G | |
624 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)(14,18)(15,17)(16,19)(20,23)(21,26)(22,24)(25,27)(28,29,32,36,33,35,41,42)(30,34,38,31,37,39,43,40);(13,17)(15,23)(18,24)(19,20)(22,27)(25,26)(28,30)(29,34)(31,36)(32,38)(33,37)(35,39)(40,42)(41,43);(12,14)(13,18)(15,22)(16,21)(17,24)(19,26)(20,25)(23,27)(28,31,32,39,33,40,41,34)(29,30,36,38,35,37,42,43);(13,19)(14,21)(17,20)(22,27)(29,35)(30,37)(36,42)(38,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 10977);