Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#3559 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
1024 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)(13,16)(14,18)(20,21)(22,29)(23,26)(24,32)(25,28)(27,33)(30,34)(31,35);(13,16)(17,19)(20,22,25,23)(21,26,28,29)(24,30,33,31)(27,34,32,35);(12,13)(14,17)(15,16)(18,19)(20,23,25,22)(21,26,28,29)(24,31,33,30)(27,34,32,35);(12,14,15,18)(13,17,16,19)(20,21)(22,29)(23,26)(24,27)(25,28)(30,35)(31,34)(32,33);(20,24)(21,27)(22,30)(23,31)(25,33)(26,34)(28,32)(29,35)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2291);