Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C59 ⋊ C4×Q32 |
150 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=e,b^2=g,c^2=eg,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,d^b=df,f^b=fg,h^b=h^58,h^c=h^58682 conjugacy classes — view the full character table.
| maximal subgroup of | #28509267, #28509271, #28509272, … |
| maximal normal subgroup of | #28509267, #28509271, #28509272, … |
| maximal quotient of | #28500422, #28500604, #28500679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6368);