Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C59 ⋊ #3296 |
408 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=e,b^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^58,d^b=de,f^c=fg760 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3296, C2×#21435931, #29465170, … |
| maximal normal subgroup of | D59×#3296, C2×#21435931, #29465170, … |
| maximal quotient of | #28604106, #28604908, #28605826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16345);