Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3198 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#21901 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C22×C22⋊C4 |
| prime radical | C11×#3455 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C11×#117 ◁ G | |
1058 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(14,18)(20,21,24,28,25,23,32,27)(22,26,31,34,30,29,35,33);(12,13)(14,17)(15,16)(18,19)(20,22)(21,26)(23,29)(24,31)(25,30)(27,33)(28,34)(32,35);(13,16)(17,19)(20,23)(21,25)(22,29)(24,27)(26,30)(28,32)(31,33)(34,35);(12,14,15,18)(13,17,16,19)(22,30)(26,29)(31,35)(33,34)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14889);