Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9103 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#10988 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| 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 | |
1274 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)(12,13)(14,15)(16,17)(18,26)(19,30,32,23)(20,33)(21,25)(22,28)(24,36)(27,44,46,43)(29,41)(31,40,35,42)(34,38)(37,47,39,45);(16,18,21,29)(17,22,25,38)(19,27,32,46)(20,34,36,28)(23,39,30,37)(24,41,33,26)(31,47,35,45)(40,44,42,43);(13,15)(16,19)(17,23)(18,27)(20,35)(21,32)(22,37)(24,42)(25,30)(26,43)(28,47)(29,46)(31,36)(33,40)(34,45)(38,39)(41,44)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3976);