Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3168 |
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|b^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^58,h^b=h^58,h^c=h^58856 conjugacy classes — view the full character table.
| maximal subgroup of | #28498672, #28498677, #28498690, … |
| maximal normal subgroup of | #28498672, #28498677, #28498690, … |
| maximal quotient of | #28589234, #28592896, #28592905, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15083);