Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18992 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19010 |
| 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 | |
920 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,22)(15,21)(16,20)(17,19)(18,23)(24,27)(25,26)(29,34)(31,32)(35,42)(36,39)(37,40)(41,43);(12,14)(13,18)(15,25)(16,23)(17,24)(19,26)(20,27)(21,22)(28,29)(30,35)(31,34)(32,39)(33,36)(37,41)(38,43)(40,42);(12,14)(13,18)(15,23)(16,25)(17,24)(19,26)(20,22)(21,27)(28,30)(29,35)(31,37)(32,40)(33,38)(34,41)(36,43)(39,42);(13,19)(18,26)(20,21)(22,27)(28,31,33,32)(29,34,36,39)(30,37,38,40)(35,41,43,42)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11998);