Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1655 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#8504 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | #379 |
| prime radical | C11×#3529 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G | |
728 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16,17,18)(20,21)(22,30,33,26)(23,34,35,45)(24,29)(25,28)(27,36,42,38)(31,47)(32,44,37,41)(39,43)(40,49)(46,50)(48,51);(12,13)(14,18)(15,17)(16,19)(20,22)(21,26)(23,31)(24,37)(25,33)(27,40)(28,30)(29,44)(32,39)(34,47)(35,48)(36,50)(38,49)(41,43)(42,46)(45,51);(14,19)(16,18)(20,23)(21,27)(22,31)(24,38)(25,35)(26,40)(28,42)(29,45)(30,46)(32,50)(33,48)(34,43)(36,39)(37,49)(41,47)(44,51)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1492);