Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#9996 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
686 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,16)(15,18)(17,19)(20,21)(22,30)(23,28)(24,27)(25,29)(26,31)(32,35)(33,34);(13,16)(14,19)(17,18)(20,22)(21,26)(23,33)(24,31)(25,32)(27,35)(28,30)(29,34);(21,27)(23,24)(26,30)(28,29)(31,33)(34,35)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2984);