Finite Group DatabasebetaFinite Group Databasebeta| order | 18786 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C101 · Schur multiplier (H2) = C1 |
| direct product | C101×D31⋊C3 |
| unambiguous semidirect product | D31⋊(C3×C101) |
| unambiguous semidirect product | (C31⋊C3)⋊(C2×C101) |
| unambiguous semidirect product | (D31×C101)⋊C3 |
| Fitting, socle, Hall | C31×C101 ⋊ C2×C3 |
| derived, Sylow | C31 ⋊ C2×C3×C101 |
| Hall | C31⋊C3×C101 ⋊ C2 |
| Hall | D31×C101 ⋊ C3 |
| Hall | C31⋊C3 ⋊ C2×C101 |
| Hall | D31 ⋊ C3×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C101 | D31⋊C3 |
| commutator, cosocle, hypocenter | C31 | C2×C3×C101 |
| Frattini | C1 | G |
| Fitting, socle | C31×C101 | C2×C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C101 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3131 |
1111 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31⋊C3×D101, C2×C101×D31⋊C3 |
| maximal normal subgroup of | D31⋊C3×D101, C2×C101×D31⋊C3 |
| maximal quotient of | C101×(C31⋊C3)⋊C4, C2×C101×D31⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18786, 11);