Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C43 ⋊ #2029 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13063293 |
| commutator | C24×C43 | C23 |
| Frattini | C24 | C22×D43 |
| Fitting | C43×#379 | C2 |
| socle | C22×C43 | #120 |
| hypercenter | #379 | D43 |
| hypocenter | C43 | #2029 |
| LCS | G ▷ C24×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ #379 | |
466 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 69 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=d,b^2=d,b^a=bd,c^a=ce,f^a=fg,c^b=cf,e^b=eg,h^b=h^42614 conjugacy classes — view the full character table.
| maximal subgroup of | #24984175, #24984177, #25009314, … |
| maximal normal subgroup of | #24984175, #24984177, #25009314, … |
| maximal quotient of | #24999565, #24999567, #24999570, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 5674);