Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×C5⋊#11759817 |
| unambiguous semidirect product | (C2×C5)⋊(C3×#11759817) |
| Fitting, socle | C2×C3×C5×C132 ⋊ C2×C3 |
| derived, Hall | C5×C132 ⋊ C22×C32 |
| Hall | C3×C5×#92788 ⋊ C22 |
| Hall | C2×C13×D65 ⋊ C32 |
| Hall | C3×#92788 ⋊ C2×D5 |
| Sylow | C132 ⋊ C2×C32×D5 |
| Sylow | C5 ⋊ C2×C3×#11759817 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C5⋊#11759817 |
| commutator, cosocle, hypocenter | C5×C132 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C132 | C2×C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C2×C3 | |
384 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 780 |
948 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 750);