Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | D4×Q8×C43 ⋊ C2 |
| Sylow | C43 ⋊ #3520 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D43 |
| commutator, socle | C22×C43 | C25 |
| Fitting | D4×Q8×C43 | C2 |
| hypercenter | D4×Q8 | D43 |
| hypocenter | C43 | #3520 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1124 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=f,e^2=fg,b^a=bf,c^a=cg,e^a=ef,h^a=h^42,d^b=df,h^c=h^42,h^e=h^42569 conjugacy classes — view the full character table.
| maximal subgroup of | #25073218, #25073229, #25073306, … |
| maximal normal subgroup of | #25073218, #25073229, #25073306, … |
| maximal quotient of | #25256805, #25257315, #25257345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 18560);