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×C4 |
| direct product | C11×#2821 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C11 |
| prime radical | C24×C11 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
430 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17,19,21)(18,20,22,23)(25,29)(30,32)(31,35)(38,39);(13,15)(18,22)(20,23)(24,25)(26,32)(27,35)(28,29)(30,34)(31,37)(33,38)(36,39);(12,13)(14,15)(16,17)(18,20)(19,21)(22,23)(24,26,28,34)(25,30,29,32)(27,36,37,33)(31,39,35,38);(16,18)(17,20)(19,22)(21,23)(24,27,28,37)(25,31,29,35)(26,33,34,36)(30,38,32,39)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 1553);