Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C59×#452 ⋊ C2 |
| Sylow | C59 ⋊ #3278 |
482 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,c^b=cg,d^b=de,e^b=eg,e^d=eg,h^d=h^58580 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3278, C2×#21435755, #29463862, … |
| maximal normal subgroup of | D59×#3278, C2×#21435755, #29463862, … |
| maximal quotient of | #28580015, #28580131, #28580141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16169);