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×#3507 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| prime radical | C11×#532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
1012 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)(14,18)(16,19)(20,21)(22,29)(23,24)(25,26)(27,32)(28,33)(30,35)(31,34);(12,13,15,17)(14,16,18,19)(21,26)(23,28)(27,29)(30,34);(12,14,15,18)(13,16,17,19)(20,22,25,32)(21,27,26,29)(23,30,28,34)(24,31,33,35);(20,23,25,28)(21,24,26,33)(22,30,32,34)(27,31,29,35);(20,24)(21,28)(22,31)(23,26)(25,33)(27,34)(29,30)(32,35)484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2239);