Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C11×C22⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ #2561 |
672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=fg,b^2=eg,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^10238 conjugacy classes — view the full character table.
| maximal subgroup of | #14651207, #14651227, #14654166, … |
| maximal normal subgroup of | #14651207, #14651227, #14654166, … |
| maximal quotient of | #14675994, #14676536, #14676583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 9663);