Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33764 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#33789 |
| 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 ◁ C11×#117 ◁ C11×#405 ◁ G | |
562 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)(14,18)(15,17)(16,19)(20,21,26,31)(22,27,33,48)(23,36,39,70)(24,40,44,69)(25,45,42,30)(28,51,53,37)(29,54,56,43)(32,58,59,81)(34,64,62,80)(35,67,63,50)(38,71,46,55)(41,57,72,52)(47,73,74,60)(49,77,76,66)(61,82,68,78)(65,79,83,75);(12,14,15,19)(13,16,17,18)(20,22)(21,27)(23,32)(24,34)(25,35)(26,33)(28,47)(29,49)(30,50)(31,48)(36,58)(37,60)(38,61)(39,59)(40,64)(41,65)(42,63)(43,66)(44,62)(45,67)(46,68)(51,73)(52,75)(53,74)(54,77)(55,78)(56,76)(57,79)(69,80)(70,81)(71,82)(72,83);(14,19)(16,18)(20,23,26,39)(21,28,31,53)(22,32,33,59)(24,41,44,72)(25,46,42,38)(27,47,48,74)(29,55,56,71)(30,57,45,52)(34,65,62,83)(35,68,63,61)(36,69,70,40)(37,54,51,43)(49,78,76,82)(50,79,67,75)(58,80,81,64)(60,77,73,66);(13,17)(16,18)(22,33)(27,48)(32,59)(34,62)(35,63)(47,74)(49,76)(50,67)(58,81)(60,73)(61,68)(64,80)(65,83)(66,77)(75,79)(78,82)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26777);