Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | D3×#2171 |
| Fitting | C3×#2171 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2171 |
654 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#12068, #72222653, D3×#33443, … |
| maximal normal subgroup of | D3×#12068, D3×#33443, C2×D3×#2171 |
| maximal quotient of | #72222653, D3×#12062, C2×D3×#2171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322798);