Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#70050 |
| Fitting | C2×C3×#410 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2008 |
2118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10826597, C2×D3×#2008, C2×#10826598, … |
| maximal normal subgroup of | C2×#10826597, C2×D3×#2008, C2×#10826598, … |
| maximal quotient of | #72254079, #72254113, #72272252 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 196560);