Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#71715 |
| Fitting | C2×C3×#525 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2010 |
2190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#2010, C2×#10909603, C2×#10909604, … |
| maximal normal subgroup of | C2×D3×#2010, C2×#10909603, C2×#10909604, … |
| maximal quotient of | #72255196, #72255206, #72255220 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 196584);