Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C11×#131 ⋊ 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^a=h^10,f^c=fg232 conjugacy classes — view the full character table.
| maximal subgroup of | #14670729, #14670731, #14670785, … |
| maximal normal subgroup of | #14670729, #14670731, #14670785, … |
| maximal quotient of | #14736015, #14736043, #14736083, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 14230);