Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×SD16×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3394 |
372 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,b^2=eg,c^2=e,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^58,d^b=de,f^c=fg,h^d=h^58847 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3394, C2×#21437093, #29469630, … |
| maximal normal subgroup of | D59×#3394, C2×#21437093, #29469630, … |
| maximal quotient of | #28605486, #28605504, #28607523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17507);