Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#2514 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C11 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
372 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(14,18)(20,21,25,23)(22,27,26,24)(30,34)(32,35);(12,13,16,15)(14,17,18,19)(20,22)(21,24)(23,27)(25,26)(28,29,31,33)(30,35,34,32);(12,14)(13,17)(15,19)(16,18)(20,23,25,21)(22,27,26,24)(28,30,31,34)(29,32,33,35);(12,15,16,13)(14,19,18,17)(20,24,25,27)(21,26,23,22)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 1246);