Finite Group DatabasebetaFinite Group Databasebeta| order | 18270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | D45×C29⋊C7 |
| unambiguous semidirect product | C5⋊(D9×C29⋊C7) |
| unambiguous semidirect product | C9⋊(D5×C29⋊C7) |
| unambiguous semidirect product | (C29×D45)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C9×C29 | C2×C7 |
| Frattini | C3 | D15×C29⋊C7 |
| socle | C3×C5×C29 | D3×C7 |
| LCS | G ▷ C5×C9×C29 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1305 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D45×D29⋊C7, D45⋊(D29⋊C7), D5×D9×C29⋊C7, … |
| maximal normal subgroup of | D45×D29⋊C7, D45⋊(D29⋊C7), D5×D9×C29⋊C7, … |
| maximal quotient of | Dic45×C29⋊C7, C2×D45×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18270, 24);