Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#13408 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C22×C11×D8 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
482 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(17,18)(20,21,26,32)(22,27,31,25)(23,28,24,33)(29,35,30,34);(16,17)(18,19)(20,22)(21,27)(23,29)(24,30)(25,32)(26,31)(28,35)(33,34);(13,15)(16,18,19,17)(21,28)(22,30)(23,34)(24,35)(25,27)(29,31)(32,33)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6396);