Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ #2984 |
364 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 179 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=f,b^2=e,c^2=e,f^2=g,b^a=be,d^a=de,c^b=ceg,h^b=h^10,h^d=h^10250 conjugacy classes — view the full character table.
| maximal subgroup of | #14724959, #14724961, #14724967, … |
| maximal normal subgroup of | #14724959, #14724961, #14724967, … |
| maximal quotient of | #14752514, #14752835, #14752843, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13598);