Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×2−1+4×C43 ⋊ C2 |
| Sylow | C43 ⋊ #3499 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D43 |
| commutator, socle | C22×C43 | C25 |
| Fitting | C2×2−1+4×C43 | C2 |
| hypercenter | C2×2−1+4 | D43 |
| hypocenter | C43 | #3499 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
1476 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=f,c^2=g,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^c=h^42758 conjugacy classes — view the full character table.
| maximal subgroup of | #25012172, #25105790, #25105792, … |
| maximal normal subgroup of | #25012172, #25105790, #25105792, … |
| maximal quotient of | #25256697, #25256968, #25256989, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 18291);