Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#23842 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C11×#376 ◁ G | |
662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,19)(14,18,15,17)(20,21,24,27)(22,26,23,25)(28,29)(30,33)(31,35)(32,34)(36,40)(37,42)(38,41)(39,43);(12,14,16,15)(13,17,19,18)(20,22,24,23)(21,25,27,26)(28,30)(29,33)(31,36)(32,38)(34,41)(35,40)(37,39)(42,43);(12,14,16,15)(13,18,19,17)(20,23,24,22)(21,26,27,25)(30,36)(31,39)(33,40)(35,43)(37,38)(41,42);(12,15,16,14)(13,17,19,18)(29,34)(33,41)(35,43)(40,42)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16830);