Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#556 ⋊ C2 |
| Sylow | C59 ⋊ #3376 |
346 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,b^2=e,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^58754 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3376, C2×#21436917, #29468497, … |
| maximal normal subgroup of | D59×#3376, C2×#21436917, #29468497, … |
| maximal quotient of | #28605354, #28605560, #28607682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17331);