Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×#41×C43 ⋊ C2 |
| Sylow | C43 ⋊ #3481 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D43 |
| commutator, socle | C22×C43 | C25 |
| Frattini | C22 | C24×D43 |
| Fitting | C4×#41×C43 | C2 |
| hypercenter | C4×#41 | D43 |
| hypocenter | C43 | #3481 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C4×#41 | |
1242 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|e^2=fg,b^a=bf,c^a=cg,h^a=h^42,d^b=df,h^c=h^42890 conjugacy classes — view the full character table.
| maximal subgroup of | #24988645, #24988646, #25063564, … |
| maximal normal subgroup of | #24988645, #24988646, #25063564, … |
| maximal quotient of | #25256039, #25256049, #25256062, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 18120);