Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3178 |
350 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^58,c^b=cg,d^b=dg,h^b=h^58844 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3178, C2×#21434768, #29458581, … |
| maximal normal subgroup of | D59×#3178, C2×#21434768, #29458581, … |
| maximal quotient of | #28589272, #28592979, #28592991, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15182);