Finite Group DatabasebetaFinite Group Databasebeta| order | 38220 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×ΓL(1,𝔽8)⋊Dic65 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C7×Dic65) |
104 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5460 |
2338 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38220, 300);