Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#2176 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C11 | C2×D8 |
| commutator | C8 | C22×C4×C11 |
| Frattini, cosocle | C2×C8 | C23×C11 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C42×C11 ◁ C4×C8×C11 ◁ G | |
148 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17)(18,26)(19,30)(20,35)(21,23)(22,27)(24,33)(25,32)(28,46)(29,43)(31,41)(34,42)(36,40)(37,45)(38,47)(39,44);(16,18,21,29)(17,22,23,37)(19,31,34,47)(20,36,32,28)(24,40,39,46)(25,41,35,38)(26,42,43,30)(27,44,45,33);(12,14,15,13)(17,23)(22,37)(24,39)(25,35)(26,43)(30,42)(38,41)(40,46)352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 908);