Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3 |
| Fitting, socle, Hall | C5×C132 ⋊ C32×C4 |
| derived, Sylow | C132 ⋊ C32×C4×C5 |
| Hall | C5×C13⋊C32 ⋊ C4 |
| Hall | C5×C13×#261 ⋊ C32 |
| Hall | C13⋊C32 ⋊ C4×C5 |
| Hall | C13×#261 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C13⋊C3×AGL(1,𝔽13) |
| commutator, hypocenter | C132 | C32×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C132 | C32×C4 |
| prime radical | C5×C13⋊C3×D13⋊C3 | C2 |
| cosocle | C13×D13 | C2×C32×C5 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C5 | |
148 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 780 |
455 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 459);