Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C27 · Schur multiplier (H2) = C1 |
| direct product | C3⋊C8×C27 |
| unambiguous semidirect product | C3⋊(C8×C27) |
| derived | C3 ⋊ C8×C27 |
| Sylow | C3×C27 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C27 | D3 |
| commutator, hypocenter | C3 | C8×C27 |
| Frattini | C4×C9 | C3×D3 |
| Fitting | C3×C4×C27 | C2 |
| socle, prime radical | C2×C32 | C4×C9 |
| cosocle | C3×C4×C9 | C2×C3 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C4×C27 | |
41 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13046389, C3⋊C8×D27, (C3⋊D27)⋊C8, … |
| maximal normal subgroup of | #13046389, C3⋊C8×D27, (C3⋊D27)⋊C8, … |
| maximal quotient of | C27×C3⋊C16, C2×C3⋊C8×C27, C27×C9⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 17);