Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#2863 |
| 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 | |
408 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 1408 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,16)(14,19,15,18)(20,21,24,27)(22,25,26,23)(30,34)(32,35);(12,14,17,15)(13,18,16,19)(20,22,24,26)(21,25,27,23)(28,29,31,33)(30,32,34,35);(12,15,17,14)(13,19,16,18)(20,23,24,25)(21,26,27,22);(12,16,17,13)(14,19,15,18)(20,21)(22,25)(23,26)(24,27)(28,30)(29,32)(31,34)(33,35)484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 1595);