Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (ΓL(1,𝔽8)⋊D7)⋊D55 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C11 | C22×C3 |
| LCS | G ▷ C5×C72×C11 | |
| UCS | C1 | |
168 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2310 |
Polycyclic presentation:
2^2,3,5,7^2,11|d^a=d^4,e^a=e^6,g^a=g^10,e^b=e^6,f^b=f^6,f^c=f^2629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 407);