Finite Group DatabasebetaFinite Group Databasebeta| order | 36540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C7⋊#19104887 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C7×C29 | C4 |
| prime radical, cosocle | C7×C29×C3⋊D15 | C2 |
| LCS | G ▷ C32×C5×C7×C29 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6090 |
Polycyclic presentation:
2^2,3^2,5,7,29|a^2=b,c^a=cd,d^a=cd^2,e^a=e^2,f^a=f^6,g^a=g^28,c^b=c^2,d^b=d^2,e^b=e^42439 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36540, 370);