Finite Group DatabasebetaFinite Group Databasebeta| order | 31518 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C17 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (D103⋊C9)⋊C17 |
| unambiguous semidirect product | (D103⋊C17)⋊C9 |
| unambiguous semidirect product | ((C103⋊C9)⋊C17)⋊C2 |
| derived, Sylow | C103 ⋊ C2×C9×C17 |
| Hall | (C103⋊C9)⋊C17 ⋊ C2 |
| Hall | D103⋊C17 ⋊ C9 |
| Hall | D103⋊C9 ⋊ C17 |
| Hall | C103⋊C17 ⋊ C2×C9 |
| Hall | C103⋊C9 ⋊ C2×C17 |
| Hall | D103 ⋊ C9×C17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | AGL(1,𝔽103) |
| commutator, hypocenter | C103 | C2×C9×C17 |
| Fitting, socle, cosocle | C3×C103 | C2×C3×C17 |
| prime radical | C3×D103⋊C17 | C3 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 927 |
Polycyclic presentation:
2,3,17,103,3|b^3=e,d^a=d^102,d^b=d^56,d^c=d^72309 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31518, 18);