Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8491 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#8501 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #379 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C11×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
616 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)(12,13,16,23,19,14,25,29)(15,31,34,64,36,56,66,63)(17,22,38,50,42,28,53,60)(18,24,39,21,43,30,54,27)(20,44,46,73,26,55,45,40)(32,65,35,49,37,70,69,59)(33,47,67,52,68,57,72,62)(41,51,71,48,74,61,75,58);(12,14)(13,19)(15,26)(16,21)(17,22)(18,30)(20,36)(23,39)(24,43)(25,27)(28,42)(29,54)(31,33)(32,45)(34,52)(35,57)(37,46)(38,58)(40,49)(41,51)(44,63)(47,69)(48,53)(50,75)(55,64)(56,68)(59,73)(60,71)(61,74)(62,66)(65,67)(70,72);(12,15,18,35)(13,20,24,47)(14,26,30,57)(16,37,39,34)(17,40,41,33)(19,36,43,69)(21,46,23,52)(22,49,51,31)(25,32,54,66)(27,45,29,62)(28,59,61,56)(38,67,71,44)(42,73,74,68)(48,70,50,64)(53,72,75,55)(58,65,60,63)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1489);