Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C233 ⋊ #101 |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,233|a^2=d,b^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^144,d^b=de,f^d=f^232475 conjugacy classes — view the full character table.
| maximal subgroup of | #28417343, #28417344, #28417345, … |
| maximal normal subgroup of | #28417343, #28417344, #28417345, … |
| maximal quotient of | #28417280, #28417281, #28417292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 207);