Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1406 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C4 |
| direct product | C11×#1407 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #353 |
| commutator | C42 | C2×C4×C11 |
| Frattini, cosocle | #124 | C22×C11 |
| prime radical | C2×D4×C11 | D4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C11 ◁ C2×C4×C11 ◁ C11×#124 ◁ G | |
98 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)(14,22,24,37)(15,26,27,42)(16,29,31,20)(17,21)(18,23,32,39)(19,28)(25,35,30,38)(33,40,34,41)(36,43);(12,14,17,25)(13,18,21,34)(15,23,27,41)(16,30,31,24)(19,35,36,22)(20,32,29,33)(26,38,42,37)(28,39,43,40)154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 139);