Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#25000 |
| 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 ◁ C2×C4×Q8×C11 ◁ G | |
630 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)(12,13,15,16)(14,18,19,17)(20,21)(22,24)(23,25)(26,27)(28,29,31,33)(30,34,37,40)(32,35,38,41)(36,43,39,42);(13,16)(17,18)(20,22,23,26)(21,24,25,27)(29,33)(30,36)(32,38)(34,42)(37,39)(40,43);(21,25)(24,27)(28,30,31,37)(29,34,33,40)(32,39,38,36)(35,42,41,43);(12,14,15,19)(13,17,16,18)(29,33)(34,40)(35,41)(42,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17988);