Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C49⋊C3)⋊D37) |
| unambiguous semidirect product | (C49⋊C3)⋊D111 |
| Fitting, derived | C3×C37×C49 ⋊ C2×C3 |
| Hall | C3×C37×C49⋊C3 ⋊ C2 |
| Hall | C37×C49 ⋊ C3×D3 |
| Hall | C3×C49⋊C3 ⋊ D37 |
| Sylow | C49 ⋊ C3×D111 |
| Sylow | C37 ⋊ C3⋊(D49⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C37×C49 | C2×C3 |
| Frattini | C7 | C3⋊(ΓL(1,𝔽8)⋊D37) |
| socle | C3×C7×C37 | AGL(1,𝔽7) |
| LCS | G ▷ C3×C37×C49 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5439 |
Polycyclic presentation:
2,3^2,7,37,7|d^7=f^6,c^a=c^2,d^a=d^6f,e^a=e^36,f^a=f^6,d^b=d^2f^3,f^b=f^21059 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 61);