Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24986 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#24986 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #555 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | #2420 |
| prime radical | C11×#3067 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G | |
642 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)(14,25)(15,29)(16,20)(17,34)(18,23)(19,24)(21,32)(22,28)(26,35)(27,36)(30,37)(31,39)(33,38)(40,41)(42,43);(12,14,17,16,19,28,18,27)(13,20,23,25,24,36,34,22)(15,30,32,26,33,41,31,42)(21,37,29,43,39,40,38,35);(12,15)(13,21)(14,26)(16,30)(17,31)(18,32)(19,33)(20,35)(22,37)(23,38)(24,39)(25,40)(27,41)(28,42)(29,34)(36,43);(12,16,17,28,19,27,18,14)(13,22,23,20,24,25,34,36)(15,30,31,42,33,41,32,26)(21,37,38,35,39,40,29,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17974);