Finite Group DatabasebetaFinite Group Databasebeta| order | 36162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C41⋊(D49⋊C3)) |
| unambiguous semidirect product | C41⋊(C3⋊(D49⋊C3)) |
| unambiguous semidirect product | (C49⋊C3)⋊D123 |
| unambiguous semidirect product | D6027⋊C3 |
| Fitting, derived | C3×C41×C49 ⋊ C2×C3 |
| Hall | C3×C41×C49⋊C3 ⋊ C2 |
| Hall | C41×C49 ⋊ C3×D3 |
| Hall | C3×C49⋊C3 ⋊ D41 |
| Sylow | C49 ⋊ C3×D123 |
| Sylow | C41 ⋊ C3⋊(D49⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C41×C49 | C2×C3 |
| Frattini | C7 | C3⋊(ΓL(1,𝔽8)⋊D41) |
| socle | C3×C7×C41 | AGL(1,𝔽7) |
| LCS | G ▷ C3×C41×C49 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6027 |
Polycyclic presentation:
2,3^2,7,41,7|d^7=f^6,c^a=c^2,d^a=d^6f,e^a=e^40,f^a=f^6,d^b=d^2f^3,f^b=f^21173 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36162, 18);