Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8325 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#11007 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #379 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1270 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,27)(19,32,35,41)(20,36)(21,25)(22,26)(23,29)(24,34,39,33)(28,37,45,47)(30,38)(31,40)(42,44,46,43);(12,13)(14,15)(16,18,22,31)(17,23,26,38)(19,28,35,45)(20,30,21,29)(24,37,39,47)(25,40,36,27)(32,42,41,46)(33,44,34,43);(13,15)(16,19)(17,24)(18,28)(20,34)(21,33)(22,35)(23,37)(25,41)(26,39)(27,42)(29,44)(30,43)(31,45)(32,36)(38,47)(40,46)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3995);