Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C59 ⋊ #1282 |
228 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 85 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=e,d^2=g,e^2=g,b^a=bc,c^a=cf,h^a=h^58,d^b=df,h^b=h^581204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#1282, C2×#21421944, #28478339, … |
| maximal normal subgroup of | D59×#1282, C2×#21421944, #28478339, … |
| maximal quotient of | #28475218, #28475230, #28475239, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2358);