Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#69987 |
| Sylow | C3 ⋊ C2×#2091 |
1102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#2091, C2×#10909603, C2×#10909604, … |
| maximal normal subgroup of | C2×D3×#2091, C2×#10909603, C2×#10909604, … |
| maximal quotient of | #72271480, #72271483 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 199315);