Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#2100 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
214 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 100 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 — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,18)(14,19,15,17)(20,21)(22,24)(23,25)(26,27);(12,14,16,15)(13,17,18,19)(20,22,23,26)(21,24,25,27)(28,29,31,34)(30,32,35,33);(12,15,16,14)(13,17,18,19)(21,25)(24,27)(29,32)(30,35)(33,34)352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 832);