Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#446 ⋊ C2 |
| Sylow | C11 ⋊ Q8×M16 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=e,c^2=ef,f^2=g,b^a=be,d^a=dg,d^c=dg,h^c=h^10,h^d=h^10190 conjugacy classes — view the full character table.
| maximal subgroup of | #14724694, #14724700, #14724705, … |
| maximal normal subgroup of | #14724694, #14724700, #14724705, … |
| maximal quotient of | #14751763, #14751765, #14752421, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13462);