Finite Group DatabasebetaFinite Group Databasebeta| order | 612 |
| isoclinism | isoclinic class of D3×D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D51 |
| unambiguous semidirect product | (C3×D3)⋊D17 |
| unambiguous semidirect product | (D3×C17)⋊D3 |
| Fitting, socle, derived, Hall | C32×C17 ⋊ C22 |
| Sylow | C17 ⋊ D32 |
| Sylow | C32 ⋊ C2×D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C17 | C22 |
| LCS | G ▷ C32×C17 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 102 |
81 conjugacy classes — view the full character table.
| maximal subgroup of | D32×D17, C2×D3×D51, D3×D153, … |
| maximal normal subgroup of | D32×D17, C2×D3×D51, C3×D3×D51, … |
| maximal quotient of | Dic3×D51, D3×Dic51, #11927507, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(612, 28);