Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#72092 |
| Sylow | C3 ⋊ C2×#2048 |
1450 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#2048, C2×#10909602, C2×#10909603, … |
| maximal normal subgroup of | C2×D3×#2048, C2×#10909602, C2×#10909603, … |
| maximal quotient of | #72270421, #72271300 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 197395);