Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #3415 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#3415 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C22×D8 |
| commutator, Frattini, cosocle | C8 | C24×C11 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C11×#41 ◁ C11×#131 ◁ G | |
370 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 180 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)(14,19)(15,18)(16,29)(17,22)(20,26)(21,27)(23,33)(24,30)(25,39)(28,32)(31,40)(34,38)(35,37)(36,41)(42,43);(13,18)(15,26)(16,27)(19,30)(20,21)(22,32)(24,38)(25,37)(28,40)(29,31)(33,41)(34,35)(36,43)(39,42);(12,14)(13,19)(15,24)(16,25)(17,23)(18,30)(20,34)(21,35)(22,33)(26,38)(27,37)(28,36)(29,39)(31,42)(32,41)(40,43);(14,23)(19,33)(24,36)(25,37)(30,41)(34,42)(35,39)(38,43)352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2147);