Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #532×D43 |
| Fitting | C43×#532 ⋊ C2 |
| Sylow | C43 ⋊ C2×#532 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D43 |
| commutator, socle | C22×C43 | C25 |
| Frattini | C22 | C24×D43 |
| Fitting | C43×#532 | C2 |
| hypercenter | #532 | D43 |
| hypocenter | C43 | C2×#532 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
1728 conjugacy classes of subgroups.
644 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1480, D43×#1484, #25063135, … |
| maximal normal subgroup of | D43×#1480, D43×#1484, #25063135, … |
| maximal quotient of | D43×#2285, D43×#2293, D43×#2297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17787);