Finite Group DatabasebetaFinite Group Databasebeta| order | 32012 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C151⋊#6157 |
| Fitting, socle, derived, Hall | C53×C151 ⋊ C4 |
| Sylow | C151 ⋊ #6157 |
| Sylow | C53 ⋊ Dic151 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C53×C151 | C4 |
| prime radical, cosocle | D53×C151 | C2 |
| LCS | G ▷ C53×C151 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8003 |
Polycyclic presentation:
2^2,53,151|a^2=b,c^a=c^30,d^a=d^150,c^b=c^522117 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32012, 7);