Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17603 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#17609 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#525 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G | |
944 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)(13,18,20,32)(15,26)(19,31,35,42)(21,33,22,27)(24,39)(28,30)(34,40,36,43)(37,41);(12,13,16,21)(14,19,25,36)(15,27,26,32)(17,22,29,20)(18,30,33,28)(23,34,38,35)(24,40,39,42)(31,41,43,37);(12,14,16,25)(13,19,21,36)(15,24,26,39)(17,23,29,38)(18,31,33,43)(20,35,22,34)(27,40,32,42)(28,37,30,41);(14,23)(19,34)(24,37)(25,38)(31,40)(35,36)(39,41)(42,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 10597);