Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | D42×D43 |
| Fitting | D42×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×D42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D43 |
| commutator, socle | C22×C43 | C25 |
| Fitting | D42×C43 | C2 |
| hypercenter | D42 | D43 |
| hypocenter | C43 | C2×D42 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ D42 | |
2536 conjugacy classes of subgroups.
575 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1619, D43×#1629, D43×#1639, … |
| maximal normal subgroup of | D43×#1619, D43×#1629, D43×#1639, … |
| maximal quotient of | D4×C22⋊C4×D43, D4×C4⋊C4×D43, D43×#2358, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17945);