Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D55⋊#64418 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C11×#3862 | C22 |
| Fitting, socle | C5×C72×C11 | C2×D3 |
| LCS | G ▷ C5×C11×#3862 | |
| UCS | C1 | |
136 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 770 |
Polycyclic presentation:
2^2,3,5,11,7^2|d^a=d^4,e^a=e^10,c^b=c^2,d^b=d^4,f^b=f^2g^3,g^b=f^6g^5,f^c=f^4g^4,g^c=g^2370 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 375);