Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2069 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11138 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #396 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1439 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
864 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,22)(15,26,29,19)(16,30)(17,21)(18,24)(20,32)(23,39,27,37)(25,38)(28,35,31,36)(33,41,43,40)(34,42);(12,14,16,24,17,25,32,42)(13,18,20,22,21,34,30,38)(15,27,28,41,29,23,31,40)(19,33,35,39,26,43,36,37);(12,15)(13,19)(14,23)(16,31)(17,29)(18,33)(20,36)(21,26)(22,37)(24,41)(25,27)(28,32)(30,35)(34,43)(38,39)(40,42)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4126);