Finite Group DatabasebetaFinite Group Databasebeta| order | 31518 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊(D103⋊C17)) |
| unambiguous semidirect product | (C103⋊C17)⋊(C3⋊D3) |
| unambiguous semidirect product | (C3⋊D309)⋊C17 |
| Fitting, socle, derived, Hall | C32×C103 ⋊ C2×C17 |
| Hall | C32×C103⋊C17 ⋊ C2 |
| Hall | C3⋊D309 ⋊ C17 |
| Hall | C103⋊C17 ⋊ C3⋊D3 |
| Sylow | C103 ⋊ C17×C3⋊D3 |
| Sylow | C32 ⋊ D103⋊C17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C103 | C2×C17 |
| LCS | G ▷ C32×C103 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 927 |
Polycyclic presentation:
2,17,3^2,103|c^a=c^2,d^a=d^2,e^a=e^102,e^b=e^72129 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31518, 27);