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×#2834 |
| 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 | |
372 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(17,19)(20,21)(22,24)(23,25)(26,27)(28,29,32,34)(30,31,33,35);(14,18)(17,19)(20,21,23,25)(22,26,27,24)(28,30)(29,31)(32,33)(34,35);(12,13,15,16)(14,17,18,19)(20,21)(22,26)(23,25)(24,27)(28,31)(29,33)(30,34)(32,35);(12,14)(13,17)(15,18)(16,19)(20,22)(21,24)(23,27)(25,26)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 1566);