Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C43×M64 ⋊ C2 |
| Sylow | C43 ⋊ #2263 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D688 |
| commutator | C16×C43 | C23 |
| Frattini | C16 | C22×D43 |
| Fitting | C43×M64 | C2 |
| socle | C2×C43 | C2×D16 |
| hypercenter | M64 | D43 |
| hypocenter | C43 | #2263 |
| LCS | G ▷ C16×C43 ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ M64 | |
112 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,h^a=h^42,d^b=de,e^b=ef,f^b=fg,h^b=h^42866 conjugacy classes — view the full character table.
| maximal subgroup of | #25017221, #25017224, #25017271, … |
| maximal normal subgroup of | #25017221, #25017224, #25017271, … |
| maximal quotient of | #25017037, #25017041, #25017104, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6825);