Finite Group DatabasebetaFinite Group Databasebeta| order | 21018 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C113 · Schur multiplier (H2) = C1 |
| direct product | C113×D31⋊C3 |
| unambiguous semidirect product | D31⋊(C3×C113) |
| unambiguous semidirect product | (C31⋊C3)⋊(C2×C113) |
| unambiguous semidirect product | (D31×C113)⋊C3 |
| Fitting, socle, Hall | C31×C113 ⋊ C2×C3 |
| derived, Sylow | C31 ⋊ C2×C3×C113 |
| Hall | C31⋊C3×C113 ⋊ C2 |
| Hall | D31×C113 ⋊ C3 |
| Hall | C31⋊C3 ⋊ C2×C113 |
| Hall | D31 ⋊ C3×C113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C113 | D31⋊C3 |
| commutator, cosocle, hypocenter | C31 | C2×C3×C113 |
| Frattini | C1 | G |
| Fitting, socle | C31×C113 | C2×C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C113 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3503 |
1243 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21018, 11);