Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×#108×C59 ⋊ C2 |
| Sylow | C59 ⋊ #1929 |
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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=f,b^2=df,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^b=h^58,e^c=eg,h^c=h^58850 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1929, C2×#21424743, #28591192, … |
| maximal normal subgroup of | D59×#1929, C2×#21424743, #28591192, … |
| maximal quotient of | #28486861, #28486868, #28486875, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 5157);