Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C4 |
| direct product | C11×#1411 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #353 |
| commutator | C42 | C2×C4×C11 |
| Frattini, cosocle | C4⋊Q8 | C22×C11 |
| prime radical | C22×C11 | #99 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C11 ◁ C2×C4×C11 ◁ C11×C4⋊Q8 ◁ G | |
94 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)(12,13,15,20,17,22,29,39)(14,23,24,37,26,34,41,42)(16,21,31,38,32,19,28,36)(18,27,33,30,35,40,43,25);(12,14,17,26)(13,18,22,35)(15,27,29,40)(16,30,32,25)(19,34,21,23)(20,37,39,42)(24,28,41,31)(33,38,43,36)187 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 143);