Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C43 ⋊ #2183 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D43 |
| commutator, socle | C22×C43 | C22×C8 |
| Fitting | C8×Q8×C43 | C2 |
| hypercenter | C8×Q8 | D43 |
| hypocenter | C43 | #2183 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C8 ◁ C8×Q8 | |
126 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^42,h^c=h^42896 conjugacy classes — view the full character table.
| maximal subgroup of | #25008367, #25008371, #25008381, … |
| maximal normal subgroup of | #25008367, #25008371, #25008381, … |
| maximal quotient of | #25011946, #25011952, #25014214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6419);