Finite Group DatabasebetaFinite Group Databasebeta| order | 1872 |
| isoclinism | isoclinic class of C3⋊D3×#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C3×C4 |
| direct product | C3⋊Dic3×#261 |
| unambiguous semidirect product | (C3×#261)⋊Dic3 |
| derived, Hall | C32×C13 ⋊ C42 |
| Sylow | C13 ⋊ C4×C3⋊Dic3 |
| Sylow | C32 ⋊ C4×#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D3×#261 |
| commutator, hypocenter | C32×C13 | C42 |
| Fitting, socle | C2×C32×C13 | C2×C4 |
| prime radical, cosocle | C2×C32×D13 | C22 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 ◁ C2 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 468 |
84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1872, 628);