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×#3491 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| prime radical | C11×#534 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
1052 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)(14,18)(16,19)(20,21)(22,26)(23,30)(24,25)(27,31)(28,34)(29,32)(33,35);(12,13,15,17)(14,16,18,19)(21,25)(26,32)(27,30)(33,34);(12,14)(13,16)(15,18)(17,19)(20,22,24,29)(21,26,25,32)(23,28,31,35)(27,33,30,34);(20,21)(22,26)(23,27)(24,25)(28,33)(29,32)(30,31)(34,35);(20,23)(21,27)(22,28)(24,31)(25,30)(26,33)(29,35)(32,34)484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2223);