Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#3502 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| prime radical | C23×C11 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
964 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,17)(14,18,19,16)(20,21,25,29)(22,27,23,26)(24,28,32,35)(30,34,31,33);(20,22,25,23)(21,26,29,27)(24,31,32,30)(28,34,35,33);(12,14,15,19)(13,16,17,18)(20,23,25,22)(21,27,29,26)(24,31,32,30)(28,34,35,33);(20,24,25,32)(21,28,29,35)(22,30,23,31)(26,33,27,34);(20,21)(22,26)(23,27)(24,28)(25,29)(30,33)(31,34)(32,35)484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2234);