Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19014 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19040 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
872 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)(13,18)(14,21)(15,16)(20,23)(22,24)(25,27)(28,29)(30,37)(31,35)(32,41)(33,36)(34,39)(38,42)(40,43);(12,13,17,20)(14,19,22,26)(15,23,16,18)(21,27,24,25)(28,30,33,40)(29,34,36,42)(31,39,32,38)(35,43,41,37);(12,14)(13,19)(15,21)(16,24)(17,22)(18,25)(20,26)(23,27)(28,29)(30,34)(31,35)(32,41)(33,36)(37,38)(39,43)(40,42);(13,20)(18,23)(19,26)(25,27)(28,31,33,32)(29,35,36,41)(30,38,40,39)(34,37,42,43)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12028);