Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#504 ⋊ C2 |
| Sylow | C11 ⋊ #3416 |
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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,e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,h^a=h^10,e^b=ef,f^b=fg,h^b=h^10,d^c=dg232 conjugacy classes — view the full character table.
| maximal subgroup of | #14910524, #14910526, #14910531, … |
| maximal normal subgroup of | #14910524, #14910526, #14910531, … |
| maximal quotient of | #14906686, #14906693, #14906822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17658);