Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×D8×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3102 |
396 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^58,f^c=fg850 conjugacy classes — view the full character table.
| maximal subgroup of | #28558588, #28558598, #28558641, … |
| maximal normal subgroup of | #28558588, #28558598, #28558641, … |
| maximal quotient of | #28588713, #28591619, #28591642, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14524);