Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C11×C22⋊Q8 ⋊ C2 |
| Sylow | C11 ⋊ #3056 |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=e,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,h^b=h^10172 conjugacy classes — view the full character table.
| maximal subgroup of | #14791210, #14791214, #14791232, … |
| maximal normal subgroup of | #14791210, #14791214, #14791232, … |
| maximal quotient of | #14736548, #14736570, #14736592, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 14136);