Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C4×C11×#41 ⋊ C2 |
| Sylow | C11 ⋊ #3428 |
1540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=g,e^2=f,b^a=bf,d^a=df,c^b=cf,h^d=h^10268 conjugacy classes — view the full character table.
| maximal subgroup of | #14751500, #14751503, #14753318, … |
| maximal normal subgroup of | #14751500, #14751503, #14753318, … |
| maximal quotient of | #14911985, #14912000, #14912002, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17709);