Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C11×#338 ⋊ C2 |
| Sylow | C11 ⋊ #2050 |
266 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^7,11|c^2=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fg,h^a=h^10,c^b=cf,d^b=dg,e^b=eg,h^b=h^10,e^c=eg,f^c=fg,h^c=h^10136 conjugacy classes — view the full character table.
| maximal subgroup of | #14666300, #14666305, #14666311, … |
| maximal normal subgroup of | #14666300, #14666305, #14666311, … |
| maximal quotient of | #14657454, #14657461, #14657468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5798);