Finite Group DatabasebetaFinite Group Databasebeta| order | 30972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#23780086 |
| Fitting, socle, derived, Hall | C3×C29×C89 ⋊ C4 |
| Hall | C29×C89 ⋊ Dic3 |
| Hall | C3×C89 ⋊ #1181 |
| Sylow | C89 ⋊ C3⋊#1181 |
| Hall | C3×C29 ⋊ #67063 |
| Sylow | C29 ⋊ C3⋊#67063 |
| Sylow | C3 ⋊ #23780086 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C29×C89 | C4 |
| prime radical, cosocle | C3×D2581 | C2 |
| LCS | G ▷ C3×C29×C89 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7743 |
Polycyclic presentation:
2^2,3,29,89|a^2=b,c^a=c^2,d^a=d^17,e^a=e^34,d^b=d^28,e^b=e^881941 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30972, 21);