Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#13406 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C2×C11 | #2034 |
| prime radical | C11×#3067 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C2×C11×#131 ◁ G | |
390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 75 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,25)(15,31)(16,23)(17,39)(18,24)(19,27)(20,34)(21,38)(22,37)(26,57)(28,44)(29,46)(30,45)(32,65)(33,66)(35,52)(36,64)(40,51)(41,50)(42,53)(43,62)(47,73)(48,69)(49,70)(54,68)(55,59)(56,63)(58,75)(60,74)(61,72)(67,71);(12,14)(13,19)(15,32)(16,29)(17,40)(18,30)(20,47)(21,45)(22,51)(23,25)(24,46)(26,35)(27,38)(28,42)(31,57)(33,60)(34,67)(36,58)(37,61)(39,56)(41,59)(43,48)(44,54)(49,55)(50,71)(52,75)(53,72)(62,70)(63,68)(64,74)(65,66)(69,73);(12,15,18,36)(13,20,24,49)(14,26)(16,35,38,33)(17,41,42,69)(19,43)(21,50,23,48)(22,52,54,66)(25,55)(27,32)(28,62)(29,58)(30,60)(31,53,64,39)(34,68,70,37)(40,67)(44,57)(45,47)(46,71)(51,74)(56,75)(59,63)(61,73)(65,72)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6394);