Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C22×#13063320 |
| Fitting | C22×C4⋊C4×C43 ⋊ C2 |
| Sylow | C43 ⋊ C22×#126 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D43 |
| commutator | C22×C43 | C25 |
| Frattini | C22 | C24×D43 |
| Fitting | C22×C4⋊C4×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C22×C4⋊C4 | D43 |
| hypocenter | C43 | C22×#126 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
1320 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
896 conjugacy classes — view the full character table.
| maximal subgroup of | #24987960, #24989247, #24989249, … |
| maximal normal subgroup of | #24987960, #24989247, #24989249, … |
| maximal quotient of | C22×#14582766, C22×#14582780, C22×#14582782, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17767);