Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C59×#410 ⋊ C2 |
| Sylow | C59 ⋊ #2883 |
800 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 209 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^a=be,e^a=eg,f^b=fg,d^c=dg,h^c=h^58,h^d=h^58679 conjugacy classes — view the full character table.
| maximal subgroup of | #28506273, #28506275, #28506277, … |
| maximal normal subgroup of | #28506273, #28506275, #28506277, … |
| maximal quotient of | #28554504, #28554507, #28554510, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 12969);