Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#2859 |
| 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 | |
472 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 264 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(18,21)(19,23)(24,25,29,28)(26,31,30,27);(16,17,20,22)(18,19,21,23)(24,26)(25,27)(28,31)(29,30);(12,13,14,15)(16,18,20,21)(17,19,22,23)(24,27,29,31)(25,30,28,26);(16,19)(17,21)(18,22)(20,23)(24,28,29,25)(26,31,30,27)484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 1591);