Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C59 ⋊ #1720 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14273723 |
| commutator | C42×C59 | C23 |
| Frattini | C42 | C22×D59 |
| Fitting | C59×#486 | C2 |
| socle | C22×C59 | #127 |
| hypercenter | #486 | D59 |
| hypocenter | C59 | #1720 |
| LCS | G ▷ C42×C59 ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #486 | |
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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^2=dfg,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,c^b=cf,h^b=h^58,h^c=h^58664 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1720, C2×#21423755, #28576461, … |
| maximal normal subgroup of | D59×#1720, C2×#21423755, #28576461, … |
| maximal quotient of | #28482487, #28488471, #28488478, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4169);