Finite Group DatabasebetaFinite Group Databasebeta| order | 37548 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C7⋊#19128973 |
| Fitting, socle, derived, Hall | C32×C7×C149 ⋊ C4 |
| Hall | C32×C149 ⋊ Dic7 |
| Hall | C7×C149 ⋊ #157 |
| Sylow | C149 ⋊ C7⋊#157 |
| Hall | C32×C7 ⋊ Dic149 |
| Sylow | C32 ⋊ Dic1043 |
| Sylow | C7 ⋊ #19128973 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C7×C149 | C4 |
| prime radical, cosocle | C7×C3⋊D3×C149 | C2 |
| LCS | G ▷ C32×C7×C149 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6258 |
Polycyclic presentation:
2^2,3^2,7,149|a^2=b,c^a=cd,d^a=cd^2,e^a=e^6,f^a=f^148,c^b=c^2,d^b=d^23132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37548, 86);