Finite Group DatabasebetaFinite Group Databasebeta| order | 30012 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×C3⋊#6923 |
| unambiguous semidirect product | C3⋊(C41×#6923) |
| Fitting, socle, Hall | C3×C41×C61 ⋊ C4 |
| derived, Hall | C3×C61 ⋊ C4×C41 |
| Hall | C41×C61 ⋊ Dic3 |
| Hall | C3×C41 ⋊ #6923 |
| Sylow | C61 ⋊ Dic3×C41 |
| Sylow | C3 ⋊ C41×#6923 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | C3⋊#6923 |
| commutator, hypocenter | C3×C61 | C4×C41 |
| Frattini | C1 | G |
| Fitting, socle | C3×C41×C61 | C4 |
| prime radical | C3×C41×D61 | C2 |
| cosocle | C3×D61 | C2×C41 |
| LCS | G ▷ C3×C61 | |
| UCS | C1 ◁ C41 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7503 |
2091 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30012, 31);