Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#18400 |
| 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 | |
978 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)(13,20)(14,25)(15,27)(16,30)(21,36)(22,38)(23,31)(24,37)(26,29)(28,41)(32,33)(34,43)(35,39)(40,42);(12,13)(14,21)(15,28)(16,31)(17,34)(18,23)(19,24)(20,30)(22,25)(26,41)(27,39)(29,36)(32,37)(33,43)(35,40)(38,42);(12,14,19,15)(13,21,24,28)(16,29,33,26)(17,25,18,27)(20,35,37,38)(22,23,39,34)(30,40,32,42)(31,36,43,41);(12,15,19,14)(13,22,24,39)(16,29,33,26)(17,27,18,25)(20,36,37,41)(21,23,28,34)(30,40,32,42)(31,35,43,38)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11388);