Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊(#5997⋊C3) |
| unambiguous semidirect product | (C11⋊(#5997⋊C3))⋊C5 |
| unambiguous semidirect product | ((C11⋊C5)⋊#5997)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C11 | C3×C4×C5 |
| prime radical | C11⋊C5×#64424 | C2 |
| cosocle | C11×C7⋊D7 | C2×C3×C5 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 154 |
Polycyclic presentation:
2,3,5,2,7^2,11|a^2=d,e^a=e^3f^5,f^a=e^5f^4,g^a=g^10,e^b=e^2,f^b=f^2,g^c=g^4,e^d=e^6,f^d=f^694 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 245);