Finite Group DatabasebetaFinite Group Databasebeta| order | 18786 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C101 · Schur multiplier (H2) = C1 |
| direct product | C2×C31⋊C3×C101 |
| unambiguous semidirect product | (C2×C31)⋊(C3×C101) |
| unambiguous semidirect product | (C2×C31×C101)⋊C3 |
| Fitting, socle, Hall | C2×C31×C101 ⋊ C3 |
| derived, Sylow | C31 ⋊ C2×C3×C101 |
| Hall | C31×C101 ⋊ C2×C3 |
| Hall | C2×C31 ⋊ C3×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C101 | C31⋊C3 |
| commutator, cosocle, hypocenter | C31 | C2×C3×C101 |
| Frattini | C1 | G |
| Fitting, socle | C2×C31×C101 | C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C101 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6262 |
2626 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C31⋊C3×C101, C31⋊C3×Dic101, C101×(C31⋊C3)⋊C4, … |
| maximal normal subgroup of | C4×C31⋊C3×C101, C31⋊C3×Dic101, C101×(C31⋊C3)⋊C4, … |
| maximal quotient of | C4×C31⋊C3×C101, C22×C31⋊C3×C101 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18786, 2);