Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33687 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C23×C11 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
520 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 83 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21,24,29)(22,32,34,27)(23,37,38,73)(25,43,41,72)(26,46,42,31)(28,51,52,39)(30,55,54,45)(33,61,62,71)(35,67,65,76)(36,50,66,60)(40,74,47,56)(44,57,75,53)(48,63,58,80)(49,69,59,81)(64,78,70,82)(68,77,83,79);(13,16)(17,19)(20,22)(21,27)(23,33)(24,34)(25,35)(26,36)(28,48)(29,32)(30,49)(31,50)(37,71)(38,62)(39,63)(40,64)(41,65)(42,66)(43,76)(44,68)(45,69)(46,60)(47,70)(51,80)(52,58)(53,77)(54,59)(55,81)(56,78)(57,79)(61,73)(67,72)(74,82)(75,83);(20,23,24,38)(21,28,29,52)(22,33,34,62)(25,44,41,75)(26,47,42,40)(27,48,32,58)(30,56,54,74)(31,57,46,53)(35,68,65,83)(36,70,66,64)(37,72,73,43)(39,55,51,45)(49,78,59,82)(50,79,60,77)(61,76,71,67)(63,81,80,69);(12,14,15,18)(13,17,16,19)(22,34)(27,32)(33,62)(35,65)(36,66)(48,58)(49,59)(50,60)(61,71)(63,80)(64,70)(67,76)(68,83)(69,81)(77,79)(78,82)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26675);