Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#103×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3298 |
420 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=de,h^b=h^58,f^c=fg847 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3298, C2×#21435957, #29465175, … |
| maximal normal subgroup of | D59×#3298, C2×#21435957, #29465175, … |
| maximal quotient of | #103×C22⋊D59, #28604899, #28605835, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16371);