Finite Group DatabasebetaFinite Group Databasebeta| order | 30318 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C163 · Schur multiplier (H2) = C1 |
| direct product | C163×D31⋊C3 |
| unambiguous semidirect product | D31⋊(C3×C163) |
| unambiguous semidirect product | (C31⋊C3)⋊(C2×C163) |
| Fitting, socle, Hall | C31×C163 ⋊ C2×C3 |
| derived, Sylow | C31 ⋊ C2×C3×C163 |
| Hall | C31⋊C3×C163 ⋊ C2 |
| Hall | D31×C163 ⋊ C3 |
| Hall | C31⋊C3 ⋊ C2×C163 |
| Hall | D31 ⋊ C3×C163 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C163 | D31⋊C3 |
| commutator, cosocle, hypocenter | C31 | C2×C3×C163 |
| Frattini | C1 | G |
| Fitting, socle | C31×C163 | C2×C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C163 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5053 |
1793 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30318, 18);