Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#2810 |
| 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 | |
344 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)(12,13)(14,18)(15,16)(17,19)(21,24)(22,26)(28,29,33,30)(31,35,32,34);(13,16)(14,19)(20,21,23,24)(22,27,26,25)(28,30,33,29)(31,35,32,34);(12,14)(13,17)(15,19)(16,18)(28,31,33,32)(29,34,30,35);(12,13)(14,17)(15,16)(18,19)(20,22,23,26)(21,25,24,27)(28,32,33,31)(29,35,30,34)352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 1542);