Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4×D4×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3114 |
450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 450 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|d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^58,d^c=dg,f^c=fg1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28486796, #28486802, #28561271, … |
| maximal normal subgroup of | #28486796, #28486802, #28561271, … |
| maximal quotient of | #28588740, #28591705, #28591720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14648);