Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#14583496 |
| Fitting | C22×C4⋊C4×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×#539 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D43 |
| commutator | C22×C43 | C25 |
| Frattini | C22 | C24×D43 |
| Fitting | C22×C4⋊C4×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C22×C4⋊C4 | D43 |
| hypocenter | C43 | C2×#539 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C22×C4⋊C4 | |
1144 conjugacy classes of subgroups.
884 conjugacy classes — view the full character table.
| maximal subgroup of | #24988418, #24988422, #25062626, … |
| maximal normal subgroup of | #24988418, #24988422, #25062626, … |
| maximal quotient of | C2×#19137198, C2×#19137229, C2×#19137264, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17861);