Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18977 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3547 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
866 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)(14,23)(15,20)(16,21)(17,26)(18,22)(19,24)(25,27)(28,29,34,37)(30,40,36,43)(31,41,35,42)(32,39,33,38);(12,14,18,15)(13,19,22,27)(16,24,17,25)(20,26,23,21)(28,30,34,36)(29,35,37,31)(32,42,33,41)(38,43,39,40);(12,15,18,14)(13,20,22,23)(16,24,17,25)(19,26,27,21)(28,31,34,35)(29,36,37,30)(32,40,33,43)(38,41,39,42);(12,16,18,17)(13,21,22,26)(14,24,15,25)(19,20,27,23)(29,37)(31,35)(38,39)(40,43)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11965);