Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19186 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#19225 |
| 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 | |
630 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)(13,17)(15,18)(19,23)(20,24)(22,25)(26,27)(28,29)(30,37)(31,36)(32,34)(33,40)(35,38)(39,43)(41,42);(12,13,18,24,16,20,15,17)(14,19,25,27,21,26,22,23)(29,34)(35,42)(36,40)(37,43);(12,14)(13,19)(15,22)(16,21)(17,23)(18,25)(20,26)(24,27)(28,30)(29,35)(31,38)(32,39)(33,41)(34,42)(36,43)(37,40);(14,21)(19,26)(22,25)(23,27)(28,31,32,33)(29,36,34,40)(30,38,39,41)(35,43,42,37)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12213);