Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×SD16×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3357 |
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 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=eg,b^2=g,c^2=eg,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 | #28579626, #28579628, #28579671, … |
| maximal normal subgroup of | #28579626, #28579628, #28579671, … |
| maximal quotient of | #28605140, #28605151, #28606415, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17138);