Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C59×#339 ⋊ C2 |
| Sylow | C59 ⋊ #1764 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D59 |
| commutator | C4×C59 | C2×C42 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C59×#339 | C2 |
| socle | C22×C59 | C4×D4 |
| hypercenter | #339 | D59 |
| hypocenter | C59 | #1764 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 ◁ #339 | |
300 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 105 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=e,b^2=f,c^2=e,d^2=g,e^2=g,b^a=bd,d^a=dg,f^a=fg,h^c=h^58868 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1764, C2×#21423930, #28586532, … |
| maximal normal subgroup of | D59×#1764, C2×#21423930, #28586532, … |
| maximal quotient of | #28479360, #28479370, #28479377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4344);