Finite Group DatabasebetaFinite Group Databasebeta| order | 12108 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16860937⋊C3 |
| Fitting, socle, derived, Sylow | C1009 ⋊ C3×C4 |
| Hall | #16860937 ⋊ C3 |
| Hall | C1009⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1009 | C3×C4 |
| prime radical | D1009⋊C3 | C2 |
| cosocle | D1009 | C2×C3 |
| LCS | G ▷ C1009 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,1009|a^2=c,d^a=d^540,d^b=d^374,d^c=d^100896 conjugacy classes — view the full character table.
| maximal subgroup of | #49138047, C3×#16860937⋊C3, C3⋊(#16860937⋊C3) |
| maximal normal subgroup of | #49138047, C3×#16860937⋊C3 |
| maximal quotient of | #49138023, C3×#16860937⋊C3, C3⋊(#16860937⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12108, 8);