Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4⋊C8×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2065 |
284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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=de,b^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^58,c^b=cf,d^c=dg,e^c=eg,f^c=fg,h^c=h^581192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#2065, C2×#21425469, #28617301, … |
| maximal normal subgroup of | D59×#2065, C2×#21425469, #28617301, … |
| maximal quotient of | #28493205, #28493226, #28493257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 5883);