Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C11⋊C5×#64423⋊C2 |
| unambiguous semidirect product | #64423⋊(C2×C11⋊C5) |
| unambiguous semidirect product | #64424⋊(C2×C11⋊C5) |
| unambiguous semidirect product | (C11×#64423⋊C2)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C11 | C22×C3×C5 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 | |
208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 154 |
133 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×#64423⋊C2 |
| maximal normal subgroup of | AGL(1,𝔽11)×#64423⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 261);