Finite Group DatabasebetaFinite Group Databasebeta| order | 18270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D3045 |
| unambiguous semidirect product | C3⋊(C3×D1015) |
| unambiguous semidirect product | C5⋊(C3×D609) |
| unambiguous semidirect product | C29⋊(C3×D105) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3045 |
| commutator, cosocle, hypocenter | C3×C5×C7×C29 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C29 | C2 |
| LCS | G ▷ C3×C5×C7×C29 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6090 |
4572 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D29×D105, C3×D7×D435, C3×D15×D203, … |
| maximal normal subgroup of | C3×D29×D105, C3×D7×D435, C3×D15×D203, … |
| maximal quotient of | C3×Dic3045, C2×C3×D3045 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18270, 70);