Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #1752 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D43 |
| commutator | C22×C43 | C2×C42 |
| Fitting | C2×C22⋊C8×C43 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | C2×C22⋊C8 | D43 |
| hypocenter | C43 | #1752 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C22⋊C8 | |
360 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 149 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=e,e^2=g,b^a=bd,h^a=h^42,c^b=cg,h^b=h^42,h^c=h^42896 conjugacy classes — view the full character table.
| maximal subgroup of | #24987142, #24987146, #24987147, … |
| maximal normal subgroup of | #24987142, #24987146, #24987147, … |
| maximal quotient of | #24987068, #24987072, #24987097, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4289);