Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C11⋊#15668766 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C72×C11 | C3×C4 |
| prime radical | D5×C11×#3862 | C2 |
| cosocle | C72×D5×C11 | C2×C3 |
| LCS | G ▷ C5×C72×C11 | |
| UCS | C1 | |
120 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1155 |
Polycyclic presentation:
2,3,2,5,7^2,11|a^2=c,d^a=d^2,e^a=e^6,f^a=f^6,g^a=g^10,e^b=e^2,f^b=f^4,d^c=d^4427 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 370);