Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18451 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3537 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1038 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)(12,13,17,22)(14,19,24,27)(15,21,16,20)(18,25,26,23)(28,29)(30,33)(31,34)(32,35)(36,42)(37,40)(38,41)(39,43);(12,14)(13,18)(15,23)(16,25)(17,24)(19,20)(21,27)(22,26)(28,30)(29,33)(31,36)(32,37)(34,39)(35,40)(38,43)(41,42);(12,14)(13,19)(15,25)(16,23)(17,24)(18,20)(21,26)(22,27)(28,31)(29,34)(30,36)(32,38)(33,39)(35,41)(37,43)(40,42);(12,15,17,16)(13,20,22,21)(14,23,24,25)(18,19,26,27)(29,35)(33,40)(34,41)(39,42)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11439);