Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7943 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#7943 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#95 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C25×C11 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C24×C4×C11 ◁ G | |
982 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)(14,18,19,16)(15,17)(20,21)(22,28)(23,31)(24,27)(25,30)(26,32)(29,34)(33,35);(12,14)(13,16)(15,19)(17,18)(20,22)(21,25,27,33)(23,30)(24,29)(26,28,31,34)(32,35);(14,19)(16,18)(22,29)(25,33)(28,34)(30,35)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 931);