Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #3139 |
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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=g,b^2=f,c^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^58,d^b=dg,d^c=dg1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28486210, #28486230, #28486292, … |
| maximal normal subgroup of | #28486210, #28486230, #28486292, … |
| maximal quotient of | #28588904, #28591406, #28592370, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14891);