Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C233 ⋊ C4 |
| Sylow | C233 ⋊ #99 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,233|a^2=d,b^a=bc,c^a=ce,f^a=f^144,d^b=de,f^b=f^232,f^d=f^232475 conjugacy classes — view the full character table.
| maximal subgroup of | #28417339, #28417340, #28417341, … |
| maximal normal subgroup of | #28417339, #28417340, #28417341, … |
| maximal quotient of | #28417279, #28417280, #28417287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 205);