Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18192 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18216 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
988 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,19)(14,25)(15,27)(16,30)(20,38)(21,34)(22,36)(23,31)(24,37)(28,35)(32,43)(39,40);(12,13)(14,20)(15,28)(16,31)(17,23)(18,24)(19,30)(21,27)(22,33)(25,40)(26,38)(29,35)(32,36)(34,42)(37,43)(39,41);(12,14,18,15)(13,20,24,28)(16,29,32,26)(17,25,33,27)(19,34,37,39)(21,23,40,22)(30,42,43,41)(31,35,36,38);(12,15,18,14)(13,21,24,40)(16,29,32,26)(17,27,33,25)(19,35,37,38)(20,23,28,22)(30,42,43,41)(31,34,36,39)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11204);