Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C43 ⋊ #1313 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic43 |
| commutator | C4×C43 | C4×C8 |
| Frattini | C4×C8 | C2×D43 |
| Fitting | C43×#346 | C2 |
| socle | C22×C43 | #97 |
| hypercenter | #346 | D43 |
| hypocenter | C43 | #1313 |
| LCS | G ▷ C4×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ #346 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=be,d^a=dg,c^b=cg,h^b=h^42884 conjugacy classes — view the full character table.
| maximal subgroup of | #24983932, #24983934, D43×#1313, … |
| maximal normal subgroup of | #24983932, #24983934, D43×#1313, … |
| maximal quotient of | #24983213, #24983426, #24983932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2430);