Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19086 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19093 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
782 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 75 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,18,23)(14,24,26,36)(15,28,30,37)(16,22,17,21)(19,31,34,27)(20,32,35,29)(25,33,39,43)(38,40,42,41)(44,45,49,52)(46,54,56,68)(47,51,59,66)(48,60,63,53)(50,61,65,57)(55,71,72,70)(58,69,62,67)(64,74,75,73);(12,14)(13,19)(15,25)(16,31)(17,27)(18,26)(20,33)(21,36)(22,24)(23,34)(28,42)(29,41)(30,39)(32,40)(35,43)(37,38)(44,46,49,56)(45,50,52,65)(47,55,59,72)(48,61,63,57)(51,64,66,75)(53,68,60,54)(58,74,62,73)(67,70,69,71);(12,15,18,30)(13,20,23,35)(14,25,26,39)(16,29,17,32)(19,33,34,43)(21,28,22,37)(24,38,36,42)(27,40,31,41)(44,47,49,59)(45,51,52,66)(46,55,56,72)(48,62,63,58)(50,64,65,75)(53,69,60,67)(54,70,68,71)(57,74,61,73);(14,26)(19,34)(24,36)(25,39)(27,31)(33,43)(38,42)(40,41)(45,52)(46,56)(51,66)(53,60)(55,72)(57,61)(67,69)(73,74)341 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12081);