Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C11 · Schur multiplier (H2) = C2×C8 |
| direct product | C11×#8268 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C11 | C2×D4 |
| commutator | C4 | C2×C4×C8×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | C4×C4⋊C4 |
| prime radical | C23×C11 | #117 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(21,25,27,30)(22,28)(26,33,34,32)(29,35);(12,13,14,16,15,17,18,19)(20,21)(22,26)(23,30)(24,27)(25,31)(28,34)(29,33)(32,35);(20,22,23,29,24,28,31,35)(21,26,30,33,27,34,25,32)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1256);