Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C43×#529 ⋊ C2 |
| Sylow | C43 ⋊ #3561 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D43 |
| commutator, socle | C22×C43 | C25 |
| Fitting | C43×#529 | C2 |
| hypercenter | #529 | D43 |
| hypocenter | C43 | #3561 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #529 | |
1032 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=f,d^2=g,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^42,c^b=cg,d^b=df626 conjugacy classes — view the full character table.
| maximal subgroup of | #24988900, #24988904, #24989061, … |
| maximal normal subgroup of | #24988900, #24988904, #24989061, … |
| maximal quotient of | #25259538, #25259606, #25259851, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 19080);