Finite Group DatabasebetaFinite Group Databasebeta| order | 30012 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#23756302 |
| Fitting, socle, derived, Hall | C3×C41×C61 ⋊ C4 |
| Hall | C41×C61 ⋊ Dic3 |
| Hall | C3×C61 ⋊ #4223 |
| Hall | C3×C41 ⋊ #6923 |
| Sylow | C61 ⋊ C3⋊#4223 |
| Sylow | C41 ⋊ C3⋊#6923 |
| Sylow | C3 ⋊ #23756302 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C41×C61 | C4 |
| prime radical, cosocle | C3×D2501 | C2 |
| LCS | G ▷ C3×C41×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7503 |
Polycyclic presentation:
2^2,3,41,61|a^2=b,c^a=c^2,d^a=d^32,e^a=e^50,d^b=d^40,e^b=e^601881 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30012, 34);