Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#405 ⋊ C2 |
| Sylow | C11 ⋊ #3175 |
362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|c^2=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^10,d^b=dg232 conjugacy classes — view the full character table.
| maximal subgroup of | #14908881, #14908883, #14908926, … |
| maximal normal subgroup of | #14908881, #14908883, #14908926, … |
| maximal quotient of | #14754345, #14758046, #14758054, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 15149);