Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C11×C4⋊C8 ⋊ C2 |
| Sylow | C11 ⋊ #2994 |
364 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,d^2=e,f^2=g,b^a=be,d^a=de,c^b=ceg,d^b=dg,h^b=h^10250 conjugacy classes — view the full character table.
| maximal subgroup of | #14724923, #14724927, #14724960, … |
| maximal normal subgroup of | #14724923, #14724927, #14724960, … |
| maximal quotient of | #14752577, #14752624, #14752681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13666);