Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | #518×D43 |
| Fitting | C43×#518 ⋊ C2 |
| Sylow | C43 ⋊ C2×#518 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D43 |
| commutator | C2×C43 | C24×C4 |
| Fitting | C43×#518 | C2 |
| socle | C22×C43 | C25 |
| hypercenter | #518 | D43 |
| hypocenter | C43 | C2×#518 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #518 | |
1920 conjugacy classes of subgroups.
782 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1828, D43×#1829, D43×#1856, … |
| maximal normal subgroup of | D43×#1828, D43×#1829, D43×#1856, … |
| maximal quotient of | D43×#2273, D43×#2274, D43×#2275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17693);