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×#3538 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| prime radical | C11×#525 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
1014 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)(20,21,25,27)(22,28,30,23)(24,32,33,26)(29,31,35,34);(13,16)(17,19)(20,22,25,30)(21,23,27,28)(24,29,33,35)(26,31,32,34);(12,13)(14,17)(15,16)(18,19);(12,14)(13,17)(15,18)(16,19)(20,23)(21,22)(24,31)(25,28)(26,29)(27,30)(32,35)(33,34);(20,24,25,33)(21,26,27,32)(22,29,30,35)(23,31,28,34)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2270);