Finite Group DatabasebetaFinite Group Databasebeta| order | 12102 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D2017⋊C3 |
| unambiguous semidirect product | (C2017⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C2017 ⋊ C2×C3 |
| Hall | C2017⋊C3 ⋊ C2 |
| Hall | D2017 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C2017 | C2×C3 |
| LCS | G ▷ C2017 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2017|c^a=c^2016,c^b=c^294342 conjugacy classes — view the full character table.
| maximal subgroup of | #22549029⋊C3, C2×D2017⋊C3, #31827738⋊C2, … |
| maximal normal subgroup of | #22549029⋊C3, C2×D2017⋊C3, #31827738⋊C2, … |
| maximal quotient of | Dic2017⋊C3, C2×D2017⋊C3, #31827736⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12102, 1);