Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×SD16×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2949 |
492 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=f,b^2=g,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,d^c=dg,h^d=h^58856 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2949, C2×#21432950, #29452856, … |
| maximal normal subgroup of | D59×#2949, C2×#21432950, #29452856, … |
| maximal quotient of | #28558149, #28558364, #28558373, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13364);