Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C59×#407 ⋊ C2 |
| Sylow | C59 ⋊ #2879 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C23×C4 |
| Fitting | C59×#407 | C2 |
| hypercenter | #407 | D59 |
| hypocenter | C59 | #2879 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ #407 | |
764 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 213 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,f^2=g,b^a=be,d^a=dg,c^b=cg,h^c=h^58856 conjugacy classes — view the full character table.
| maximal subgroup of | #28486325, #28486327, #28486335, … |
| maximal normal subgroup of | #28486325, #28486327, #28486335, … |
| maximal quotient of | #28554755, #28554757, #28554760, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 12953);