Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#533 ⋊ C2 |
| Sylow | C59 ⋊ #3107 |
390 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|a^2=g,b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,f^c=fg,h^c=h^58850 conjugacy classes — view the full character table.
| maximal subgroup of | #28483405, #28483411, #28483412, … |
| maximal normal subgroup of | #28483405, #28483411, #28483412, … |
| maximal quotient of | #28588720, #28591622, #28591644, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14575);