Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of D64 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#7546 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C11 | D32 |
| commutator | C32 | C2×C4×C11 |
| Frattini, cosocle | C2×C32 | C22×C11 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C4×C11 ◁ C2×C8×C11 ◁ C2×C11×C16 ◁ C2×C11×C32 ◁ G | |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 2 generators on 79 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(17,23)(18,29)(19,30)(20,34)(21,37)(24,33)(25,48)(26,52)(27,55)(28,43)(31,62)(32,47)(35,66)(36,61)(38,65)(39,40)(41,49)(42,53)(44,69)(45,46)(50,78)(51,73)(54,72)(56,57)(58,63)(59,60)(64,75)(67,76)(68,74)(70,79)(71,77);(16,17,24,44,19,25,45,72,34,49,75,78,60,68,63,55,21,27,47,74,35,50,31,41,38,54,57,48,61,69,18,23,22,28,29,40,36,51,56,52,65,77,62,76,66,79,32,42,37,53,58,70,59,67,64,71,20,26,46,73,30,39,33,43)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 534);