Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#23778460 |
| Fitting, socle | C3×C5×C132 ⋊ C3×C4 |
| derived, Hall | C5×C132 ⋊ C32×C4 |
| Hall | C3×C5×#92788 ⋊ C4 |
| Hall | #16810006 ⋊ C32 |
| Hall | C3×#92788 ⋊ AGL(1,𝔽5) |
| Sylow | C132 ⋊ C32×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C3×#14523148 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #23778460 |
| commutator, hypocenter | C5×C132 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C132 | C3×C4 |
| prime radical | C3×C5⋊#11759817 | C2 |
| cosocle | C13×D65 | C2×C32 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C3 | |
180 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 780 |
264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 541);