Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×#611 |
| Fitting | C22×C32×C9 ⋊ C2 |
| Sylow | C32×C9 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C32 | C2×D9 |
| commutator, cosocle | C2×C9 | C22×C32 |
| Frattini | C2×C3 | C2×C32×D3 |
| Fitting | C22×C32×C9 | C2 |
| socle | C2×C33 | C2×D3 |
| hypercenter | C22×C32 | D9 |
| hypocenter | C9 | C32×D4 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2×C32 ◁ C22×C32 | |
224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#88658, C3×#88663, C3×D3×#611, … |
| maximal normal subgroup of | C3×#88658, C3×#88663, C3×D3×#611, … |
| maximal quotient of | C32×Dic9⋊C4, C32×(C2×D9)⋊C4, C32×#3672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 459);