Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#1332 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | D8 |
| commutator | C8 | C2×C8×C11 |
| Frattini, cosocle | C4×C8 | C22×C11 |
| socle, prime radical | C22×C11 | #102 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C42×C11 ◁ C4×C8×C11 ◁ G | |
98 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)(12,13,14,16,15,17,18,19)(21,25)(22,28)(23,30)(26,35)(27,34)(29,32)(31,33);(20,21,24,27)(22,29,31,35)(23,32,30,26)(25,33,34,28)484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 64);