Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C233 ⋊ C2 |
| Sylow | C233 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,233|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^232,d^b=de1171 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28416601, #28416602, #28416606, … |
| maximal normal subgroup of | #28416601, #28416602, #28416606, … |
| maximal quotient of | #28416434, #28416440, #28416475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 172);