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) = C24 |
| direct product | C11×#11288 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator | C24 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #385 |
| prime radical | C24×C11 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
602 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)(16,17,20,25,21,24,33,39)(18,22,28,36,27,35,31,40)(19,23,30,38,29,37,32,41)(26,34,43,45,42,46,44,47);(12,13)(14,15)(16,18)(17,22,24,35)(19,26,29,42)(20,31)(21,27)(23,34)(25,40,39,36)(28,33)(30,44,32,43)(37,46)(38,47)(41,45);(13,15)(16,19)(17,23,24,37)(18,26,27,42)(20,32)(21,29)(22,34)(25,41,39,38)(28,44,31,43)(30,33)(35,46)(36,47)(40,45)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4276);