Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C43 ⋊ C4×#106 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D43 |
| commutator | C4×C43 | C2×C42 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#340 | C2 |
| socle | C23×C43 | C2×D4 |
| hypercenter | #340 | D43 |
| hypocenter | C43 | C4×#106 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
280 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|a^2=e,b^2=f,c^2=de,d^2=g,e^2=g,b^a=bd,d^b=dg,e^b=eg,h^c=h^42644 conjugacy classes — view the full character table.
| maximal subgroup of | #25006998, #25007000, #25007011, … |
| maximal normal subgroup of | #25006998, #25007000, #25007011, … |
| maximal quotient of | #24987777, #24987785, #24987803, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4398);