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×#3515 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
1014 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)(17,19)(20,21,25,26)(22,23,27,30)(24,32,33,28)(29,35,34,31);(21,26)(23,30)(28,32)(31,35);(12,13)(14,17)(15,16)(18,19)(20,22,25,27)(21,23,26,30)(24,29,33,34)(28,31,32,35);(20,23)(21,27)(22,26)(24,31)(25,30)(28,34)(29,32)(33,35);(12,14,15,18)(13,17,16,19)(20,24)(21,28)(22,29)(23,31)(25,33)(26,32)(27,34)(30,35)484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2247);