Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C59 ⋊ #2026 |
258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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=d,b^2=dg,c^2=g,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^58,c^b=cf,e^c=eg,h^c=h^581192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#2026, C2×#21425248, #28615983, … |
| maximal normal subgroup of | D59×#2026, C2×#21425248, #28615983, … |
| maximal quotient of | #28491685, #28491695, #28491722, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 5662);