Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C4 |
| direct product | C2×#80305 |
| Fitting | C2×C3×B(4,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ C2×#3027 |
5110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10949265, C2×#10949263, C2×D3×#3027, … |
| maximal normal subgroup of | C2×#10949265, C2×#10949263, C2×D3×#3027, … |
| maximal quotient of | #72271878, #72271879, #72272027 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1036300);