Finite Group DatabasebetaFinite Group Databasebeta| order | 37674 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#13109897 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C23⋊#10587717 |
| commutator, hypocenter | C7×C13×C23 | C2×C9 |
| Fitting, socle, cosocle | C3×C7×C13×C23 | C2×C3 |
| prime radical | C3×C7×D299 | C3 |
| LCS | G ▷ C7×C13×C23 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18837 |
Polycyclic presentation:
2,3,7,13,23,3|b^3=f,d^a=d^12,e^a=e^22,c^b=c^2,d^b=d^91161 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37674, 32);