Finite Group DatabasebetaFinite Group Databasebeta| order | 18786 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C31⋊C3×D101 |
| unambiguous semidirect product | C101⋊(C2×C31⋊C3) |
| unambiguous semidirect product | (C31×D101)⋊C3 |
| Fitting, socle, derived, Hall | C31×C101 ⋊ C2×C3 |
| Hall | C31⋊C3×C101 ⋊ C2 |
| Hall | C31×D101 ⋊ C3 |
| Sylow | C101 ⋊ C2×C31⋊C3 |
| Sylow | C31 ⋊ C3×D101 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C101 | C2×C3 |
| LCS | G ▷ C31×C101 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3131 |
676 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C31⋊C3)⋊#87938, D31⋊C3×D101, C31⋊C3×#87938, … |
| maximal normal subgroup of | (C31⋊C3)⋊#87938, D31⋊C3×D101, C31⋊C3×#87938, … |
| maximal quotient of | C31⋊C3×Dic101, C2×C31⋊C3×D101 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18786, 10);