Finite Group DatabasebetaFinite Group Databasebeta| order | 30012 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#23756303 |
| Fitting, socle, Hall | C3×C41×C61 ⋊ C4 |
| derived, Hall | C41×C61 ⋊ C3×C4 |
| Hall | C3×C61 ⋊ #4223 |
| Hall | C3×C41 ⋊ #6923 |
| Sylow | C61 ⋊ C3×#4223 |
| Sylow | C41 ⋊ C3×#6923 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #23756303 |
| commutator, hypocenter | C41×C61 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C41×C61 | C4 |
| prime radical | C3×D2501 | C2 |
| cosocle | D2501 | C2×C3 |
| LCS | G ▷ C41×C61 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7503 |
1887 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30012, 27);