Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C43 ⋊ #1839 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D43 |
| commutator | C22×C43 | C22×C8 |
| Fitting | C43×#336 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | #336 | D43 |
| hypocenter | C43 | #1839 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
240 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 105 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=f,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^c=h^42896 conjugacy classes — view the full character table.
| maximal subgroup of | #24984616, #24984618, #24984621, … |
| maximal normal subgroup of | #24984616, #24984618, #24984621, … |
| maximal quotient of | #24990314, #24990315, #24990316, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4652);