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×#3518 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
1010 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)(20,21,26,24)(22,29,23,27)(25,32,33,28)(30,34,31,35);(20,22,26,23)(21,27,24,29)(25,30,33,31)(28,34,32,35);(12,13)(14,17)(15,16)(18,19)(20,23,26,22)(21,27,24,29)(25,31,33,30)(28,34,32,35);(20,24,26,21)(22,27,23,29)(25,32,33,28)(30,34,31,35);(12,14,15,18)(13,17,16,19)(20,25)(21,28)(22,30)(23,31)(24,32)(26,33)(27,34)(29,35)484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2250);