Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C13×D195 |
| unambiguous semidirect product | (C2×C3)⋊(C3×C13×D65) |
| unambiguous semidirect product | (C2×C5)⋊(C3×C13×D39) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C13 | D195 |
| commutator, cosocle, hypocenter | C3×C5×C13 | C22×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C5×C132 | C2 |
| LCS | G ▷ C3×C5×C13 | |
| UCS | C1 ◁ C2×C3×C13 | |
320 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 780 |
7722 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 935);