Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊#10596873 |
| unambiguous semidirect product | (C11⋊#10596873)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C11⋊C5)⋊#64423 |
| commutator, hypocenter | C72×C11 | C3×C4×C5 |
| Fitting, socle, cosocle | C2×C72×C11 | C2×C3×C5 |
| prime radical | C2×C11⋊C5×#3861 | C2 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C2 | |
144 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 308 |
Polycyclic presentation:
2,3,5,7^2,11,2|a^2=g,d^a=d^6,f^a=f^10,d^b=d^2,e^b=e^2,f^c=f^4208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 147);