Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | #442×D43 |
| Fitting | C43×#442 ⋊ C2 |
| Sylow | C43 ⋊ C2×#442 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D43 |
| commutator | C4×C43 | C23×C4 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#442 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #442 | D43 |
| hypocenter | C43 | C2×#442 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #442 | |
608 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
506 conjugacy classes — view the full character table.
| maximal subgroup of | D43×AGL(1,ℤ/16), C2×#442×D43, D43×#2943, … |
| maximal normal subgroup of | D43×AGL(1,ℤ/16), C2×#442×D43, D43×#2943, … |
| maximal quotient of | D43×#1580, D43×#1586, D43×#1594, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13299);