Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C43 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D43 |
| commutator, socle | C2×C43 | C24×C4 |
| Fitting | C43×#585 | C2 |
| hypercenter | #585 | D43 |
| hypocenter | C43 | #3573 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ #585 | |
1424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=f,f^2=g,h^a=h^42,e^b=eg,d^c=dg782 conjugacy classes — view the full character table.
| maximal subgroup of | #25102554, #25102560, #25102565, … |
| maximal normal subgroup of | #25102554, #25102560, #25102565, … |
| maximal quotient of | #25960018, #25960053, #25960234, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 19222);