Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×ΓL(1,𝔽8)⋊Dic7 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(Dic7×C11⋊C5) |
| unambiguous semidirect product | (C11×ΓL(1,𝔽8)⋊Dic7)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊C5×ΓL(1,𝔽8)⋊D7 |
| commutator, hypocenter | C72×C11 | C3×C4×C5 |
| Fitting, socle, cosocle | C2×C72×C11 | C2×C3×C5 |
| prime radical | C2×C7×ΓL(1,𝔽8)×C11⋊C5 | C2 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 924 |
308 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 152);