Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33741 |
| 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 | |
484 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)(20,21,26,31)(22,27,33,46)(23,36,40,65)(24,41,43,69)(25,44,42,30)(28,49,51,38)(29,52,53,37)(32,54,56,76)(34,61,59,82)(35,62,60,48)(39,68,67,64)(45,70,71,57)(47,74,73,55)(50,66,63,75)(58,81,80,78)(72,79,77,83);(13,16)(17,19)(20,22,26,33)(21,27,31,46)(23,32,40,56)(24,34,43,59)(25,35,42,60)(28,45,51,71)(29,47,53,73)(30,48,44,62)(36,54,65,76)(37,55,52,74)(38,57,49,70)(39,58,67,80)(41,61,69,82)(50,72,63,77)(64,78,68,81)(66,79,75,83);(20,23,37,66,25,39,43,49,26,40,52,75,42,67,24,38)(21,28,41,64,30,50,53,65,31,51,69,68,44,63,29,36)(22,32,55,79,35,58,59,70,33,56,74,83,60,80,34,57)(27,45,61,78,48,72,73,76,46,71,82,81,62,77,47,54);(12,14,15,18)(13,17,16,19)(22,33)(27,46)(32,56)(34,59)(35,60)(45,71)(47,73)(48,62)(54,76)(55,74)(57,70)(58,80)(61,82)(72,77)(78,81)(79,83)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26729);