Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C11×#104 ⋊ C2 |
| Sylow | C11 ⋊ #3018 |
724 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^7,11|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^10,e^b=eg,f^b=fg,e^c=eg,h^c=h^10172 conjugacy classes — view the full character table.
| maximal subgroup of | #14759732, #14759737, #14759743, … |
| maximal normal subgroup of | #14759732, #14759737, #14759743, … |
| maximal quotient of | #14725881, #14725932, #14725983, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13861);