Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33676 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
548 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21,26,31)(22,27,35,43)(23,29,25,39)(24,28,38,45)(30,36,44,37)(32,41,34,49)(33,40,48,51)(42,46,50,47);(13,16)(17,19)(20,22,26,35)(21,27,31,43)(23,32,25,34)(24,33,38,48)(28,40,45,51)(29,41,39,49)(30,42,44,50)(36,46,37,47);(21,28)(23,25)(24,37)(27,40)(29,30)(31,45)(32,34)(33,47)(36,38)(39,44)(41,42)(43,51)(46,48)(49,50);(12,14,15,18)(13,17,16,19)(20,23,26,25)(21,29,31,39)(22,32,35,34)(24,36,38,37)(27,41,43,49)(28,44,45,30)(33,46,48,47)(40,50,51,42)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26664);