Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#70885 |
| Fitting | C2×C3×C4×D8 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2177 |
798 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#2177, C2×#10707070, C2×#10707069, … |
| maximal normal subgroup of | C2×D3×#2177, C2×#10707070, C2×#10707069 |
| maximal quotient of | C2×#11797804, C2×#10715810, C2×#10715812 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322869);