Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2021 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#10996 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator | C24 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #379 |
| prime radical | C11×#3449 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
1306 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)(16,17,20,25,21,24,33,38)(18,26,29,39,28,22,32,35)(19,23,31,36,30,37,43,47)(27,34,42,45,41,40,44,46);(12,13)(14,15)(16,18)(17,22)(19,27)(20,32)(21,28)(23,34)(24,26)(25,39)(29,33)(30,41)(31,44)(35,38)(36,46)(37,40)(42,43)(45,47);(13,15)(16,19)(17,23)(18,27)(20,31)(21,30)(22,34)(24,37)(25,36)(26,40)(28,41)(29,42)(32,44)(33,43)(35,45)(38,47)(39,46)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3984);