Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#11003 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #392 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1438 |
| prime radical | C11×#3449 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
1292 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)(14,23)(15,27,30,38)(16,31)(17,21)(18,22)(19,25)(20,29,37,28)(24,36,41,33)(26,34)(32,35)(39,40,43,42);(12,14)(13,19)(15,24)(16,32)(17,25)(18,26)(20,36)(21,34)(22,35)(23,31)(27,43)(28,42)(29,40)(30,41)(33,37)(38,39);(12,15)(13,20)(14,24)(16,29)(17,28)(18,30)(19,33)(21,38)(22,37)(23,39)(25,42)(26,41)(27,31)(32,40)(34,43)(35,36)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3991);