Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C43 ⋊ #1274 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic43 |
| commutator | C4×C43 | C4×C8 |
| Frattini | C2×C42 | C2×D43 |
| Fitting | C43×#431 | C2 |
| socle | C22×C43 | #95 |
| hypercenter | #431 | D43 |
| hypocenter | C43 | #1274 |
| LCS | G ▷ C4×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ #431 | |
168 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 77 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=e,c^2=f,d^2=g,b^a=bc,e^a=ef,d^b=df,h^b=h^42884 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1274, C2×#19132423, #24985994, … |
| maximal normal subgroup of | D43×#1274, C2×#19132423, #24985994, … |
| maximal quotient of | C43⋊#7014, #24983128, #24983130, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2338);