Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C59×#448 ⋊ C2 |
| Sylow | C59 ⋊ D4×SD16 |
546 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,e^d=eg,h^d=h^58586 conjugacy classes — view the full character table.
| maximal subgroup of | D4×SD16×D59, C2×#21435785, #29463977, … |
| maximal normal subgroup of | D4×SD16×D59, C2×#21435785, #29463977, … |
| maximal quotient of | #28578154, #28578159, #28578169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16199);