Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#137×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3063 |
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,d^c=dg,h^c=h^58670 conjugacy classes — view the full character table.
| maximal subgroup of | #28636685, #28636688, #28636700, … |
| maximal normal subgroup of | #28636685, #28636688, #28636700, … |
| maximal quotient of | #28572178, #28572200, #28572222, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14195);