Finite Group DatabasebetaFinite Group Databasebeta| order | 12108 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic1009 |
| derived, Sylow | C1009 ⋊ C3×C4 |
| Hall | C3×C1009 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D1009 |
| commutator, hypocenter | C1009 | C3×C4 |
| Frattini | C2 | C3×D1009 |
| Fitting, socle, prime radical | C2×C3×C1009 | C2 |
| cosocle | C2×C1009 | C2×C3 |
| LCS | G ▷ C1009 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
3036 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49138017, C9×Dic1009, C3×Dic1009⋊C3, … |
| maximal normal subgroup of | #49138017, C9×Dic1009, C3×Dic1009⋊C3, … |
| maximal quotient of | C9×Dic1009, C3×Dic3027, C32×Dic1009 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12108, 5);