Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | D4×Q8×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3266 |
494 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^58,d^b=de,e^b=eg,e^d=eg,h^d=h^58754 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3266, C2×#21435607, #29463765, … |
| maximal normal subgroup of | D59×#3266, C2×#21435607, #29463765, … |
| maximal quotient of | #28578067, #28578187, #28578322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16021);