Finite Group DatabasebetaFinite Group Databasebeta| order | 18726 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D3121⋊C3 |
| unambiguous semidirect product | (C3121⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C3121 ⋊ C2×C3 |
| Hall | C3121⋊C3 ⋊ C2 |
| Hall | D3121 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3121 | C2×C3 |
| LCS | G ▷ C3121 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3121 |
Polycyclic presentation:
2,3,3121|c^a=c^3120,c^b=c^1999526 conjugacy classes — view the full character table.
| maximal subgroup of | #27159676⋊C3, C2×D3121⋊C3 |
| maximal normal subgroup of | #27159676⋊C3, C2×D3121⋊C3 |
| maximal quotient of | Dic3121⋊C3, C2×D3121⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18726, 1);