Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#3028 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×#120 |
| commutator, Frattini, cosocle | C23 | C24×C11 |
| prime radical | C11×#585 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
716 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,21)(14,18,24,31)(15,19,26,33)(16,27,28,20)(22,34,36,29)(23,37,38,30)(25,39,40,32)(35,41,43,42);(12,14)(13,18)(15,22)(16,23)(17,24)(19,29)(20,30)(21,31)(25,35)(26,36)(27,37)(28,38)(32,41)(33,34)(39,42)(40,43);(12,15)(13,19)(14,22)(16,25)(17,26)(18,29)(20,32)(21,33)(23,35)(24,36)(27,39)(28,40)(30,41)(31,34)(37,42)(38,43);(12,16,17,28)(13,20,21,27)(14,23,24,38)(15,25,26,40)(18,30,31,37)(19,32,33,39)(22,35,36,43)(29,41,34,42)319 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 1760);