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 ⋊ #3529 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D43 |
| commutator, socle | C22×C43 | C25 |
| Frattini | C22 | C24×D43 |
| Fitting | C43×#529 | C2 |
| hypercenter | #529 | D43 |
| hypocenter | C43 | #3529 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ #529 | |
1058 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|e^2=f,b^a=bf,c^a=cg,d^a=dfg,c^b=cfg,d^b=df,h^b=h^42,h^d=h^42626 conjugacy classes — view the full character table.
| maximal subgroup of | #24989028, #24989031, #25077749, … |
| maximal normal subgroup of | #24989028, #24989031, #25077749, … |
| maximal quotient of | #25259208, #25259214, #25259215, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 18649);