Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19050 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19066 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
852 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)(12,13,17,20)(14,21,23,26)(15,19,16,24)(18,25,27,22)(28,29,33,30)(31,38,39,43)(32,37,42,35)(34,41,36,40);(12,14)(13,18)(15,22)(16,25)(17,23)(19,26)(20,27)(21,24)(28,30,33,29)(31,36,39,34)(32,35,42,37)(38,41,43,40);(15,16)(19,24)(21,26)(22,25)(28,31)(29,34)(30,36)(32,41)(33,39)(35,43)(37,38)(40,42);(12,15,17,16)(13,19,20,24)(14,22,23,25)(18,26,27,21)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12054);