Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#468 ⋊ C2 |
| Sylow | C59 ⋊ #3179 |
374 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=dg,h^d=h^58496 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3179, C2×#21434772, #29458581, … |
| maximal normal subgroup of | D59×#3179, C2×#21434772, #29458581, … |
| maximal quotient of | #28589263, #28592980, #28592992, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15186);