Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C43⋊C32) |
| Sylow | C43 ⋊ C4⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C16 | C2×D43 |
| commutator | C2×C43 | C2×C32 |
| Fitting | C4×C16×C43 | C2 |
| socle | C22×C43 | C2×C16 |
| hypercenter | C4×C16 | D43 |
| hypocenter | C43 | C4⋊C32 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C16 ◁ C4×C16 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^421424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊(C43⋊C32), #24984036, #24984038, … |
| maximal normal subgroup of | D4⋊(C43⋊C32), #24984036, #24984038, … |
| maximal quotient of | #24984263, #24984270, #24984284, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2706);