Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of C3⋊(C3⋊(C3⋊D3)) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C36 |
| direct product | C2×C5×C3⋊(C3⋊(C3⋊D3)) |
| unambiguous semidirect product | (C2×C3)⋊(C5×C3⋊(C3⋊D3)) |
| Fitting, socle | C2×C34×C5 ⋊ C2 |
| derived, Sylow | C34 ⋊ C22×C5 |
| Hall | C34×C5 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C3⋊(C3⋊(C3⋊D3)) |
| commutator, cosocle, hypocenter | C34 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C34×C5 | C2 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2×C5 | |
2120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 810 |
420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 475);