Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1909 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#9100 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C2×C4 | C22×C8×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C23×C11 | C2×C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
498 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,18,16,14,17,19)(20,21)(22,30)(23,34,36,27)(24,37)(25,29)(26,32)(28,39)(31,44,47,51)(33,45)(35,42,38,43)(40,46,50,48)(41,49);(12,14,15,19,16,13,17,18)(20,22,24,32,25,33,39,49)(21,26,28,30,29,41,37,45)(23,31,38,48,36,47,35,46)(27,40,43,44,34,50,42,51);(20,23,25,36)(21,27,29,34)(22,31,33,47)(24,38,39,35)(26,40,41,50)(28,43,37,42)(30,44,45,51)(32,48,49,46)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2088);