Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11143 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #394 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
838 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)(16,17,21,25,22,27,20,26)(18,28,32,40,31,39,30,23)(19,33,36,24,37,41,35,42)(29,44,46,43,34,38,45,47);(16,18,20,30,22,31,21,32)(17,23,25,28,27,40,26,39)(19,34,35,46,37,29,36,45)(24,38,41,47,42,44,33,43);(13,15)(16,19,22,37)(17,24,27,42)(18,29,31,34)(20,36,21,35)(23,38,40,44)(25,33,26,41)(28,43,39,47)(30,46,32,45)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4131);