Finite Group DatabasebetaFinite Group Databasebeta| order | 32412 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#24925159 |
| Fitting, socle, derived, Hall | C3×C37×C73 ⋊ C4 |
| Hall | C37×C73 ⋊ Dic3 |
| Hall | C3×C73 ⋊ #3866 |
| Hall | C3×C37 ⋊ #64408 |
| Sylow | C73 ⋊ C3⋊#3866 |
| Sylow | C37 ⋊ C3⋊#64408 |
| Sylow | C3 ⋊ #24925159 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C37×C73 | C4 |
| prime radical, cosocle | C3×D2701 | C2 |
| LCS | G ▷ C3×C37×C73 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8103 |
Polycyclic presentation:
2^2,3,37,73|a^2=b,c^a=c^2,d^a=d^31,e^a=e^46,d^b=d^36,e^b=e^722031 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32412, 77);