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×#7545 |
| 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)(18,24)(19,29)(20,33)(21,36)(25,47)(26,51)(27,54)(28,42)(30,58)(31,61)(32,46)(34,63)(35,57)(37,62)(38,39)(40,48)(41,52)(43,44)(45,59)(49,76)(50,74)(53,77)(55,56)(60,79)(64,73)(65,72)(66,68)(67,78)(69,75)(70,71);(16,17,24,39,19,25,43,51,33,48,58,73,56,65,31,41,21,27,45,67,34,49,60,69,37,53,71,74,57,66,32,42,22,28,46,68,35,50,70,77,62,75,79,76,63,78,59,54,36,52,61,72,55,64,30,40,20,26,44,47,29,38,18,23)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 533);