Finite Group DatabasebetaFinite Group Databasebeta| order | 1032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(D43⋊C3) |
| unambiguous semidirect product | D172⋊C3 |
| Fitting | C4×C43 ⋊ C2×C3 |
| Hall | D172 ⋊ C3 |
| Hall | C43⋊C3 ⋊ D4 |
| Sylow | C43 ⋊ C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D43⋊C3 |
| commutator, socle, cosocle | C2×C43 | C22×C3 |
| Fitting | C4×C43 | C2×C3 |
| hypercenter | C4 | D43⋊C3 |
| hypocenter | C43 | C3×D4 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C4 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 172 |
Polycyclic presentation:
2^2,3,2,43|b^2=d,b^a=bd,e^a=e^42,e^c=e^3643 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D43⋊C3, #72244904 |
| maximal normal subgroup of | D4×D43⋊C3, #72244904 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1032, 9);