Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C43×SD64 ⋊ C2 |
| Sylow | C43 ⋊ #2262 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D16×D43 |
| commutator | C16×C43 | C23 |
| Frattini | C16 | C22×D43 |
| Fitting | C43×SD64 | C2 |
| socle | C2×C43 | C2×D16 |
| hypercenter | SD64 | D43 |
| hypocenter | C43 | #2262 |
| LCS | G ▷ C16×C43 ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ SD64 | |
106 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|c^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,d^a=de,e^a=ef,f^a=fg,d^b=de,e^b=ef,f^b=fg,h^b=h^42,h^c=h^42437 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2262, C2×#19136903, #25254739, … |
| maximal normal subgroup of | D43×#2262, C2×#19136903, #25254739, … |
| maximal quotient of | #25017028, #25017030, #25017099, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6818);