Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18866 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18901 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3515 | 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)(14,20)(15,23)(16,18)(17,22)(19,25)(21,27)(24,26)(28,29,34,37)(30,38,35,43)(31,39,41,40)(32,36,33,42);(12,14,16,21)(13,17,18,26)(15,24,25,22)(19,27,23,20)(28,30,34,35)(29,31,37,41)(32,40,33,39)(36,43,42,38);(28,31)(29,35)(30,37)(32,38)(33,43)(34,41)(36,40)(39,42);(13,18)(14,21)(19,23)(22,24)(28,32,34,33)(29,36,37,42)(30,39,35,40)(31,38,41,43)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11889);