Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
| direct product | C24×ΓL(1,𝔽25) |
| Fitting | C24×C3×C8 ⋊ C2 |
| Sylow | C3 ⋊ C24×M16 |
13310 conjugacy classes of subgroups; only the 6571 normal subgroups are shown.
This group has 13310 conjugacy classes of subgroups — too many to draw. Only its 6571 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083324);