Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #2151 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D43 |
| commutator, socle | C22×C43 | C22×C8 |
| Fitting | C2×M32×C43 | C2 |
| hypercenter | C2×M32 | D43 |
| hypocenter | C43 | #2151 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C8 ◁ C2×M32 | |
160 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=e,b^2=d,e^2=f,f^2=g,b^a=bd,h^a=h^42,c^b=cg,h^b=h^42896 conjugacy classes — view the full character table.
| maximal subgroup of | #24984001, #25012733, #25012736, … |
| maximal normal subgroup of | #24984001, #25012733, #25012736, … |
| maximal quotient of | #25008146, #25008172, #25008206, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6270);