Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C43×#341 ⋊ C2 |
| Sylow | C43 ⋊ #1764 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D43 |
| commutator | C4×C43 | C2×C42 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#341 | C2 |
| socle | C22×C43 | C4×D4 |
| hypercenter | #341 | D43 |
| hypocenter | C43 | #1764 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 ◁ #341 | |
300 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 300 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=e,b^2=f,c^2=e,d^2=g,e^2=g,b^a=bd,d^a=dg,f^a=fg,h^b=h^42,h^c=h^42644 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1764, C2×#19134431, #25094441, … |
| maximal normal subgroup of | D43×#1764, C2×#19134431, #25094441, … |
| maximal quotient of | #24987268, #24987280, #24987285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 4346);