Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C128 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C43⋊C128 |
| derived, Sylow | C43 ⋊ C128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C64 | D43 |
| commutator, hypocenter | C43 | C128 |
| Fitting | C43×C64 | C2 |
| socle | C2×C43 | C64 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C64 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^421472 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×C128, C2×C43⋊C128, #24984507, … |
| maximal normal subgroup of | D43×C128, C2×C43⋊C128, #24984507, … |
| maximal quotient of | C43⋊C256, C2×C43⋊C128 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2329);