Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C59 ⋊ #1915 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16837281 |
| commutator | C23×C59 | C22×C4 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C59×#568 | C2 |
| socle | C2×C59 | #386 |
| hypercenter | #568 | D59 |
| hypocenter | C59 | #1915 |
| LCS | G ▷ C23×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #568 | |
308 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 89 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,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^58,d^b=dg,e^b=eg,f^b=fg,d^c=dg,f^c=fg1015 conjugacy classes — view the full character table.
| maximal subgroup of | #28504474, #28504479, #28504481, … |
| maximal normal subgroup of | #28504474, #28504479, #28504481, … |
| maximal quotient of | #28484229, #28484239, #28484682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 5062);