Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C233 ⋊ C2 |
| Sylow | C233 ⋊ #99 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,233|a^2=d,b^a=bc,c^a=ce,d^b=de,f^b=f^2321171 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×D233, C2×#21418449, #28416407, … |
| maximal normal subgroup of | #99×D233, C2×#21418449, #28416407, … |
| maximal quotient of | #28416158, #28416160, #28416168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 60);