Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C59×#518 ⋊ C2 |
| Sylow | C59 ⋊ #3042 |
494 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 149 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=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^58,d^b=dg,f^c=fg1018 conjugacy classes — view the full character table.
| maximal subgroup of | #28626079, #28626084, #28636566, … |
| maximal normal subgroup of | #28626079, #28626084, #28636566, … |
| maximal quotient of | #28573907, #28573916, #28573925, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14022);