Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3055 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#3183 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C11 |
| prime radical | C11×#469 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
370 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21)(22,26)(23,30)(24,33)(25,28)(27,31)(29,35)(32,34);(13,16)(17,19)(20,22,25,24)(21,26,28,33)(23,31,32,29)(27,34,35,30);(20,23,24,31,25,32,22,29)(21,27,26,30,28,35,33,34);(12,14,15,18)(13,17,16,19)(23,32)(27,35)(29,31)(30,34)352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 1915);