Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4⋊C8×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3246 |
392 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 137 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,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^58,c^b=ce,f^c=fg,h^c=h^581192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28489627, #28489629, #28489639, … |
| maximal normal subgroup of | #28489627, #28489629, #28489639, … |
| maximal quotient of | #28598570, #28598577, #28599061, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15827);