Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×#13063290 |
| Sylow | C43 ⋊ C42×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D43 |
| commutator | C2×C43 | C22×C42 |
| Frattini | C23 | C23×D43 |
| Fitting | C4×C4⋊C4×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C4×C4⋊C4 | D43 |
| hypocenter | C43 | C42×Q8 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C4⋊C4 | |
684 conjugacy classes of subgroups.
920 conjugacy classes — view the full character table.
| maximal subgroup of | #24987193, #24987203, #24987213, … |
| maximal normal subgroup of | #24987193, #24987203, #24987213, … |
| maximal quotient of | C4×#14582750, C4×C4⋊C4×Dic43, #25017769, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6859);