Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#22396 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C23×C11 | C23×C4 |
| prime radical | C22×D4×C11 | C2×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
738 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)(14,17)(15,18)(16,19)(20,21)(22,25)(23,24)(26,27)(28,29,32,36,33,30,34,38)(31,35,40,42,39,37,41,43);(12,14,17,13)(15,18,16,19)(28,30,32,38,33,29,34,36)(31,35,40,42,39,37,41,43);(12,15,17,16)(13,18,14,19)(21,24)(25,27)(28,31)(29,35)(30,37)(32,40)(33,39)(34,41)(36,42)(38,43);(12,16,17,15)(13,18,14,19)(20,22,23,26)(21,25,24,27)(29,30)(31,39)(36,38)(40,41)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15384);