Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11×C16 · Schur multiplier (H2) = C22 |
| direct product | C11×#12015 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C2×D4 |
| commutator | C4 | C22×C11×C16 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C22×C11 | C2×C4⋊C8 |
| prime radical | C23×C11 | C4⋊C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ C2×C4×C8×C11 ◁ G | |
246 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)(13,16)(14,18)(17,19)(20,21,22,25,23,26,28,31,24,27,29,32,30,33,34,35);(12,13,14,16,15,17,18,19);(13,17)(16,19)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5003);