Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#575 ⋊ C2 |
| Sylow | C11 ⋊ #3067 |
452 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|b^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^b=h^10,f^c=fg142 conjugacy classes — view the full character table.
| maximal subgroup of | #14760708, #14760709, #14760719, … |
| maximal normal subgroup of | #14760708, #14760709, #14760719, … |
| maximal quotient of | #14736012, #14736040, #14736080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 14227);