Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33691 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33693 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#575 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C11×#405 ◁ G | |
512 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
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)(14,19,25,41)(15,28,30,63)(16,33,36,68)(17,39,37,22)(20,44,46,31)(21,48,51,38)(24,52,54,62)(26,57,34,67)(27,60,56,43)(29,50,32,66)(35,45,64,47)(40,65,72,55)(42,70,49,59)(53,75,61,73)(58,74,69,71);(12,14,18,25)(13,19,23,41)(15,24,30,54)(16,34,36,26)(17,27,37,56)(20,40,46,72)(21,49,51,42)(22,43,39,60)(28,62,63,52)(29,61,32,53)(31,65,44,55)(33,67,68,57)(35,69,64,58)(38,70,48,59)(45,74,47,71)(50,75,66,73);(12,15)(13,20)(14,24)(16,35)(17,29)(18,30)(19,40)(21,50)(22,45)(23,46)(25,54)(26,58)(27,61)(28,33)(31,38)(32,37)(34,69)(36,64)(39,47)(41,72)(42,73)(43,74)(44,48)(49,75)(51,66)(52,57)(53,56)(55,59)(60,71)(62,67)(63,68)(65,70);(14,25)(15,29,30,32)(16,36)(19,41)(20,45,46,47)(21,51)(24,53,54,61)(27,56)(28,50,63,66)(31,35,44,64)(33,68)(38,48)(40,71,72,74)(43,60)(52,75,62,73)(55,69,65,58)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26681);