Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#19412 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
650 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)(16,25)(17,20)(18,23)(22,26)(24,27)(28,29)(30,34)(31,36)(32,41)(33,37)(35,38)(39,43)(40,42);(12,14,16,23,17,24,15,22)(13,18,19,21,20,26,25,27)(28,30)(29,34)(31,40)(32,38)(33,39)(35,41)(36,42)(37,43);(28,30)(29,35)(31,38)(32,40)(33,39)(34,41)(36,43)(37,42);(12,15,17,16)(13,19,20,25)(14,22,24,23)(18,21,26,27)(28,31,33,32)(29,36,37,41)(30,38,39,40)(34,35,43,42)539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12400);