Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18393 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#534 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
910 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
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)(28,29,33,36)(30,37,40,43)(31,35,32,41)(34,38,42,39);(12,14)(13,17)(15,24)(16,21)(18,26)(19,27)(20,23)(22,25)(28,30)(29,34)(31,39)(32,38)(33,40)(35,43)(36,42)(37,41);(28,29)(30,34)(31,35)(32,41)(33,36)(37,38)(39,43)(40,42);(13,18)(14,21)(19,23)(22,24)(28,31,33,32)(29,35,36,41)(30,38,40,39)(34,37,42,43)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11381);