Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#7472 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | D16 |
| commutator | C16 | C42×C11 |
| Frattini, cosocle | C22×C16 | C22×C11 |
| socle | C22×C11 | #366 |
| prime radical | C23×C11 | Q32 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C22×C4×C11 ◁ C22×C8×C11 ◁ C22×C11×C16 ◁ G | |
166 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1408 |
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)(16,17,20,27,24,30,23,48)(18,31,33,61,37,62,36,72)(19,28,39,56,41,58,40,73)(21,26,42,54,45,55,44,57)(22,46,43,59,47,74,38,29)(25,49,50,65,53,64,75,32)(34,60,66,77,69,78,68,52)(35,70,67,76,71,79,63,51);(13,15)(16,18,21,34,22,35,39,49,20,33,42,66,43,67,41,65,24,37,45,69,47,71,40,64,23,36,44,68,38,63,19,32)(17,25,28,51,29,52,57,72,48,75,73,79,74,78,55,62,30,53,58,76,59,77,54,61,27,50,56,70,46,60,26,31)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 460);