Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8491 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#8500 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #379 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C11×#3546 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
736 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,21,23,17)(15,20)(16,19)(18,22,26,24)(25,27)(28,29,32,35,33,37,31,36)(30,38,39,34,40,42,41,43);(12,14)(13,17)(15,22)(16,23)(18,20)(19,21)(24,25)(26,27)(28,30)(29,34)(31,41)(32,39)(33,40)(35,42)(36,38)(37,43);(12,14)(13,18)(15,24)(16,23)(17,20)(19,26)(21,27)(22,25)(29,35)(31,32)(34,42)(36,37)(38,43)(39,41)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1488);