Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C42 |
No aliases for this group.
| Fitting | C11×#390 ⋊ C2 |
| Sylow | C11 ⋊ #2309 |
1104 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 229 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=g,b^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,h^d=h^10184 conjugacy classes — view the full character table.
| maximal subgroup of | #14662884, #14663162, #14668744, … |
| maximal normal subgroup of | #14662884, #14663162, #14668744, … |
| maximal quotient of | #14675010, #14675078, #14675079, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7089);