Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C132 · Schur multiplier (H2) = C3×C13 |
| direct product | C132×C3⋊ΓL(1,𝔽16) |
| unambiguous semidirect product | C3⋊(C132×ΓL(1,𝔽16)) |
| Fitting, socle, Hall | C32×C5×C132 ⋊ C4 |
| derived, Hall | C32×C5 ⋊ C4×C132 |
| Hall | C32×C132 ⋊ AGL(1,𝔽5) |
| Hall | C5×C132 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ C132×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C132×C3⋊Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C132 | C3⋊ΓL(1,𝔽16) |
| commutator, hypocenter | C32×C5 | C4×C132 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C132 | C4 |
| prime radical | C32×D5×C132 | C2 |
| cosocle | C32×D5 | C2×C132 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C132 | |
576 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
3549 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 891);