Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3×C13 |
| direct product | D5×C3⋊(C3⋊(C13⋊D13)) |
| unambiguous semidirect product | (C3×D5)⋊(C3⋊(C13⋊D13)) |
| unambiguous semidirect product | (D5×C13)⋊(C3⋊D39) |
| Fitting, socle, derived, Hall | C32×C5×C132 ⋊ C22 |
| Hall | C32×C132 ⋊ C2×D5 |
| Hall | C5×C132 ⋊ C2×C3⋊D3 |
| Sylow | C132 ⋊ D5×C3⋊D3 |
| Hall | C32×C5 ⋊ C2×C13⋊D13 |
| Sylow | C32 ⋊ D5×C13⋊D13 |
| Sylow | C5 ⋊ C2×C3⋊(C3⋊(C13⋊D13)) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C132 | C22 |
| LCS | G ▷ C32×C5×C132 | |
| UCS | C1 | |
960 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
3048 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 916);