Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C43 ⋊ #1710 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13063321 |
| commutator | C42×C43 | C23 |
| Frattini | C42 | C22×D43 |
| Fitting | C43×#500 | C2 |
| socle | C22×C43 | #127 |
| hypercenter | #500 | D43 |
| hypocenter | C43 | #1710 |
| LCS | G ▷ C42×C43 ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #500 | |
168 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=f,b^2=dg,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^b=h^42,h^c=h^42500 conjugacy classes — view the full character table.
| maximal subgroup of | #25010906, #25010907, #25010910, … |
| maximal normal subgroup of | #25010906, #25010907, #25010910, … |
| maximal quotient of | #24990373, #24996341, #24996345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4119);