Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×D8×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3330 |
420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^58,c^b=cg,d^b=de,h^b=h^58,f^c=fg,h^d=h^58841 conjugacy classes — view the full character table.
| maximal subgroup of | #28578291, #28578293, #28578351, … |
| maximal normal subgroup of | #28578291, #28578293, #28578351, … |
| maximal quotient of | #28604343, #28605114, #28605980, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16817);