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 ⋊ #104 |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,233|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^144,c^b=ce,f^b=f^232,f^d=f^232304 conjugacy classes — view the full character table.
| maximal subgroup of | D233⋊#104, C2×#21418600, #28417432, … |
| maximal normal subgroup of | D233⋊#104, C2×#21418600, #28417432, … |
| maximal quotient of | #28417283, Q8⋊#14272345, #28417287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 211);