Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18503 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| socle | C22×C11 | C2×#120 |
| prime radical | C11×#3482 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G | |
922 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)(14,21)(15,19)(16,24)(17,20)(18,22)(23,26)(25,27)(28,29,34,39)(30,36,41,42)(31,35,40,43)(32,37,33,38);(12,14)(13,18)(15,22)(16,25)(17,23)(19,26)(20,27)(21,24)(28,30,34,41)(29,35,39,43)(31,32,40,33)(36,38,42,37);(28,31)(29,36)(30,32)(33,41)(34,40)(35,38)(37,43)(39,42);(12,15,17,16)(13,19,20,24)(14,22,23,25)(18,26,27,21)(28,32,34,33)(29,37,39,38)(30,40,41,31)(35,36,43,42)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11491);