Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#2381 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C24 |
| commutator | C22 | C23×C4×C11 |
| Frattini, cosocle | C23 | C24×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
424 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(17,20)(18,22)(25,29)(26,32)(31,34)(33,38);(17,20)(21,23)(24,25,28,29)(26,30,32,36)(27,34,35,31)(33,39,38,37);(16,17,19,20)(18,21,22,23)(24,26)(25,30)(27,33)(28,32)(29,36)(31,37)(34,39)(35,38);(16,18)(17,21)(19,22)(20,23)(24,27,28,35)(25,31,29,34)(26,33,32,38)(30,37,36,39)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 1113);