Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊#16810005 |
| unambiguous semidirect product | C3⋊(C3×#16810005) |
| Fitting, socle, Hall | C32×C5×C132 ⋊ C4 |
| derived | C3×C5×C132 ⋊ C3×C4 |
| Hall | C32×C132 ⋊ AGL(1,𝔽5) |
| Hall | C5×C132 ⋊ C3×Dic3 |
| Sylow | C132 ⋊ C3×ΓL(1,𝔽16) |
| Hall | C32×C5 ⋊ #10621730 |
| Sylow | C32 ⋊ #16810005 |
| Sylow | C5 ⋊ C3×C3⋊#10621730 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊#16810005 |
| commutator, hypocenter | C3×C5×C132 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C132 | C4 |
| prime radical | C32×C13×D65 | C2 |
| cosocle | C3×C13×D65 | C2×C3 |
| LCS | G ▷ C3×C5×C132 | |
| UCS | C1 ◁ C3 | |
148 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 780 |
1998 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 835);