Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C13 |
| direct product | C2×C5⋊(C9⋊(C13⋊D13)) |
| unambiguous semidirect product | (C2×C5)⋊(C9⋊(C13⋊D13)) |
| unambiguous semidirect product | (C2×C9)⋊(C5⋊(C13⋊D13)) |
| unambiguous semidirect product | (C2×C13)⋊D585 |
| Fitting | C2×C5×C9×C132 ⋊ C2 |
| derived, Hall | C5×C9×C132 ⋊ C22 |
| Hall | C9×C132 ⋊ C2×D5 |
| Hall | C5×C132 ⋊ C2×D9 |
| Sylow | C132 ⋊ C2×D45 |
| Hall | C5×C9 ⋊ C2×C13⋊D13 |
| Sylow | C9 ⋊ C2×C5⋊(C13⋊D13) |
| Sylow | C5 ⋊ C2×C9⋊(C13⋊D13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊(C9⋊(C13⋊D13)) |
| commutator, cosocle, hypocenter | C5×C9×C132 | C22 |
| Frattini | C3 | C2×C3⋊(C5⋊(C13⋊D13)) |
| Fitting | C2×C5×C9×C132 | C2 |
| socle | C2×C3×C5×C132 | D3 |
| LCS | G ▷ C5×C9×C132 | |
| UCS | C1 ◁ C2 | |
480 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15210 |
7608 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 375);