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×#3545 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
1060 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 352 |
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)(22,28)(23,25)(24,31)(26,29)(27,32)(30,33)(34,35);(13,16)(17,19)(21,23)(22,29)(27,31)(30,35);(12,13,15,16)(14,17,18,19)(20,22)(21,26)(23,28)(24,30)(25,29)(27,33)(31,34)(32,35);(12,14)(13,17)(15,18)(16,19)(20,23,25,21)(22,28,29,26)(24,31,32,27)(30,34,35,33);(20,24)(21,27)(22,30)(23,31)(25,32)(26,33)(28,34)(29,35)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2277);