Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×C7⋊(C11⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C11⋊(ΓL(1,𝔽8)×C7⋊AGL(1,𝔽5)) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C72×C11 | C3×C4 |
| prime radical | C7×D5×C11×ΓL(1,𝔽8) | C2 |
| cosocle | C72×D5×C11 | C2×C3 |
| LCS | G ▷ C5×C72×C11 | |
| UCS | C1 | |
104 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2310 |
785 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 358);