Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10464 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#10471 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C23×C11 | #121 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
366 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)(12,13,14,16)(15,17,19,18)(20,21)(22,31)(23,36)(24,41)(25,29)(26,30)(27,33)(28,39)(32,47)(34,43)(35,46)(37,42)(38,45)(40,50)(44,49)(48,51);(13,16)(17,18)(20,22,26,35)(21,27,30,43)(23,37,39,48)(24,34,25,33)(28,44,36,47)(29,46,41,31)(32,38,49,40)(42,50,51,45);(13,17)(15,19)(16,18)(20,23,24,38,26,39,25,40)(21,28,29,45,30,36,41,50)(22,32,33,48,35,49,34,37)(27,42,31,44,43,51,46,47)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3459);