Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#14582655 |
| Sylow | C43 ⋊ C2×H(3,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic43 |
| commutator | C4×C43 | C2×C42 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C2×#117×C43 | C2 |
| socle | C22×C43 | #95 |
| hypercenter | C2×#117 | D43 |
| hypocenter | C43 | C2×H(3,ℤ/4) |
| LCS | G ▷ C4×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#117 | |
404 conjugacy classes of subgroups.
884 conjugacy classes — view the full character table.
| maximal subgroup of | H(3,ℤ/4)×Dic43, C4×#14582655, #25001765, … |
| maximal normal subgroup of | H(3,ℤ/4)×Dic43, C4×#14582655, #25001765, … |
| maximal quotient of | C2×#19132423, C2×#19132424, #24985995, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4210);