Finite Group DatabasebetaFinite Group Databasebeta| order | 18270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×D9×C29⋊C7 |
| unambiguous semidirect product | C9⋊(C2×C5×C29⋊C7) |
| unambiguous semidirect product | (D9×C29)⋊(C5×C7) |
| unambiguous semidirect product | (C5×D9×C29)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D9×C29⋊C7 |
| commutator, cosocle, hypocenter | C9×C29 | C2×C5×C7 |
| Frattini | C3 | C5×D3×C29⋊C7 |
| Fitting | C5×C9×C29 | C2×C7 |
| socle | C3×C5×C29 | D3×C7 |
| LCS | G ▷ C9×C29 | |
| UCS | C1 ◁ C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1305 |
330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D9×D29⋊C7, D9×C5⋊(D29⋊C7), D5×D9×C29⋊C7, … |
| maximal normal subgroup of | C5×D9×D29⋊C7, D9×C5⋊(D29⋊C7), D5×D9×C29⋊C7, … |
| maximal quotient of | C5×Dic9×C29⋊C7, C2×C5×D9×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18270, 22);