Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C132 · Schur multiplier (H2) = C2×C13 |
| direct product | D3×C132×D15 |
| unambiguous semidirect product | (C3×D3)⋊(D5×C132) |
| unambiguous semidirect product | (C5×D3)⋊(D3×C132) |
| Fitting, socle, Hall | C32×C5×C132 ⋊ C22 |
| derived, Hall | C32×C5 ⋊ C22×C132 |
| Hall | C32×C132 ⋊ C2×D5 |
| Hall | C5×C132 ⋊ D32 |
| Sylow | C32 ⋊ C2×D5×C132 |
| Sylow | C5 ⋊ D32×C132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C132 | D3×D15 |
| commutator, cosocle, hypocenter | C32×C5 | C22×C132 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C132 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C132 | |
704 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 256 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5070 |
4563 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 866);