Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#2833 |
| 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 | |
332 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(17,19)(20,21,24,25)(22,26,27,23)(29,33)(34,36)(35,39)(42,43);(14,18)(17,19)(22,27)(23,26)(28,29,32,33)(30,36,38,34)(31,39,41,35)(37,42,40,43);(12,13)(14,17)(15,16)(18,19)(20,22)(21,23)(24,27)(25,26)(28,30,32,38)(29,34,33,36)(31,40,41,37)(35,43,39,42);(12,14)(13,17)(15,18)(16,19)(20,23)(21,22)(24,26)(25,27)(28,31,32,41)(29,35,33,39)(30,37,38,40)(34,42,36,43)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 1565);