Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2221 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#2223 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #466 |
| commutator, Frattini, cosocle | C2×C8 | C23×C11 |
| prime radical | C11×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C11×#131 ◁ G | |
144 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 60 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 — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,19)(14,25)(15,28)(16,17)(20,29)(21,36)(22,33)(23,32)(24,34)(26,41)(27,30)(31,37)(38,43)(39,42);(12,13,20,32,17,23,15,19,18,24,28,33,16,22,29,34)(14,21,35,43,25,37,26,31,27,38,40,36,30,39,41,42);(12,14)(13,21)(15,26)(16,30)(17,25)(18,27)(19,31)(20,35)(22,39)(23,37)(24,38)(28,40)(29,41)(32,43)(33,36)(34,42)286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 955);