Finite Group DatabasebetaFinite Group Databasebeta| order | 18270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C3 |
| direct product | C5×C3⋊D3×C29⋊C7 |
| unambiguous semidirect product | C3⋊(C5×D3×C29⋊C7) |
| unambiguous semidirect product | (C3⋊D3×C29)⋊(C5×C7) |
| unambiguous semidirect product | (C5×C3⋊D3×C29)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊D3×C29⋊C7 |
| commutator, cosocle, hypocenter | C32×C29 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C29 | C2×C7 |
| LCS | G ▷ C32×C29 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1305 |
330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#11760330⋊C7, C5×#157×C29⋊C7, #19104890⋊C7, … |
| maximal normal subgroup of | C5×#11760330⋊C7, C5×#157×C29⋊C7, #19104890⋊C7, … |
| maximal quotient of | C5×C3⋊Dic3×C29⋊C7, C2×C5×C3⋊D3×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18270, 42);