Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#383 ⋊ C2 |
| Sylow | C59 ⋊ C4×#126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator | C22×C59 | C23×C4 |
| Fitting | C59×#383 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | #383 | D59 |
| hypocenter | C59 | C4×#126 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #383 | |
516 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 189 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=ef,c^2=e,d^2=g,b^a=be,c^a=cf,h^d=h^58868 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#126×D59, C2×#21426644, #28747183, … |
| maximal normal subgroup of | C4×#126×D59, C2×#21426644, #28747183, … |
| maximal quotient of | #28509842, #28509861, #383×Dic59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7058);