Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | #568×D43 |
| Fitting | C43×#568 ⋊ C2 |
| Sylow | C43 ⋊ C2×#568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D43 |
| commutator, socle | C2×C43 | C24×C4 |
| Fitting | C43×#568 | C2 |
| hypercenter | #568 | D43 |
| hypocenter | C43 | C2×#568 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ #568 | |
1460 conjugacy classes of subgroups.
782 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1858, #25097441, D43×#1861, … |
| maximal normal subgroup of | D43×#1858, #25097441, D43×#1861, … |
| maximal quotient of | D43×#2873, D43×#2875, #568×Dic43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 19217);