Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D5×D13×C13⋊C9 |
| derived, Hall | C5×C132 ⋊ C22×C9 |
| Hall | C5×C13×C13⋊C9 ⋊ C22 |
| Hall | D5×C13×D13 ⋊ C9 |
| Hall | C13×C13⋊C9 ⋊ C2×D5 |
| Sylow | C132 ⋊ C2×C9×D5 |
| Sylow | C5 ⋊ C2×D13×C13⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D5×D13×C13⋊C3 |
| commutator, hypocenter | C5×C132 | C22×C9 |
| Fitting, socle, cosocle | C3×C5×C132 | C22×C3 |
| prime radical | C3×D5×C13×D13 | C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C3 | |
136 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1170 |
672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 285);