Finite Group DatabasebetaFinite Group Databasebeta| order | 12006 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C23 · Schur multiplier (H2) = C3 |
| direct product | C32×C23×D29 |
| unambiguous semidirect product | C29⋊(C2×C32×C23) |
| Fitting, socle, Hall | C32×C23×C29 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C32×C23 |
| Hall | C23×C29 ⋊ C2×C32 |
| Hall | C32×C29 ⋊ C2×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C23 | D29 |
| commutator, cosocle, hypocenter | C29 | C2×C32×C23 |
| Frattini | C1 | G |
| Fitting, socle | C32×C23×C29 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C32×C23 | |
48 conjugacy classes of subgroups.
3312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C23×#1181, C32×C23⋊#1181, C32×D23×D29, … |
| maximal normal subgroup of | C32×C23×#1181, C32×C23⋊#1181, C32×D23×D29, … |
| maximal quotient of | C32×C23×Dic29, C2×C32×C23×D29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12006, 20);