Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#1338 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22⋊C4 |
| commutator | C2×C4 | C2×C8×C11 |
| Frattini, cosocle | C4×C8 | C22×C11 |
| socle, prime radical | C22×C11 | C22⋊C8 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C4×C8×C11 ◁ G | |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(14,18)(17,19)(20,21,23,28,25,26,31,33,24,27,32,34,22,29,30,35);(12,13,15,17)(14,19,18,16)(20,22,24,25)(21,26,27,29)(23,31,32,30)(28,35,34,33)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 70);