Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#1418 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #357 |
| commutator | C16 | C2×C4×C11 |
| Frattini, cosocle | C2×C16 | C22×C11 |
| prime radical | C11×#508 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C2×C8×C11 ◁ C2×C11×C16 ◁ G | |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 2 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,18,19,34)(14,22)(15,27)(16,29)(20,38,37,42)(21,39,31,36)(23,28,35,33)(24,30)(25,43)(26,32)(40,41);(12,13)(14,23)(15,28)(16,31)(17,19)(18,32)(20,27)(21,29)(22,34)(24,37)(25,38)(26,35)(30,33)(36,41)(39,43)(40,42)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 150);