Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q8×C233 ⋊ C4 |
| Sylow | C233 ⋊ #103 |
42 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,233|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,f^a=f^144,c^b=ce,f^d=f^232304 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21418598, #28417425, #28417426, … |
| maximal normal subgroup of | C2×#21418598, #28417425, #28417426, … |
| maximal quotient of | Q8⋊#14272345, #28417285, #28417288, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 209);