Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #3081 |
398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 149 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=e,b^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^10,d^b=dg,f^c=fg202 conjugacy classes — view the full character table.
| maximal subgroup of | #14817198, #14817203, #14817228, … |
| maximal normal subgroup of | #14817198, #14817203, #14817228, … |
| maximal quotient of | #14753282, #14754759, #14754788, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 14341);