Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| unambiguous semidirect product | D33⋊(C5⋊(C7⋊D7)) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C72×C11 | C22 |
| LCS | G ▷ C3×C5×C72×C11 | |
| UCS | C1 | |
400 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8085 |
Polycyclic presentation:
2^2,3,5,7^2,11|d^a=d^4,e^a=e^6,f^a=f^6,g^a=g^10,c^b=c^2,d^b=d^4,e^b=e^6,f^b=f^62217 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 622);