Finite Group DatabasebetaFinite Group Databasebeta| order | 654 |
| isoclinism | isoclinic class of D109 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D109 |
| Fitting, socle, Hall | C3×C109 ⋊ C2 |
| derived, Sylow | C109 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D109 |
| commutator, cosocle, hypocenter | C109 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C109 | C2 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 327 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#89137, C3⋊#89137, D3×D109, … |
| maximal normal subgroup of | C3×#89137, C3⋊#89137, D3×D109, … |
| maximal quotient of | C3×Dic109, C2×C3×D109, C9×D109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(654, 4);