Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C11×#390 ⋊ C2 |
| Sylow | C11 ⋊ C4×#127 |
924 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=e,c^2=f,d^2=g,b^a=be,c^a=cf,h^c=h^10,h^d=h^10196 conjugacy classes — view the full character table.
| maximal subgroup of | #14641746, #14641827, #14641892, … |
| maximal normal subgroup of | #14641746, #14641827, #14641892, … |
| maximal quotient of | #14674956, #14674958, Dic11×#390, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7074);