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×#322 | C2 |
| socle | C22×C43 | #97 |
| hypercenter | #322 | D43 |
| hypocenter | C43 | #1313 |
| LCS | G ▷ C4×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ #322 | |
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,h^a=h^42,c^b=cg884 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1313, C2×#19132516, #25005596, … |
| maximal normal subgroup of | D43×#1313, C2×#19132516, #25005596, … |
| maximal quotient of | #24983214, #24983427, #24983933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2431);