Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | D3×#3459 |
| Fitting | C3×#3459 ⋊ C2 |
| Sylow | C3 ⋊ C2×#3459 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D3 |
| commutator, socle, cosocle | C22×C3 | C26 |
| Frattini | C22 | C25×D3 |
| Fitting | C3×#3459 | C2 |
| hypercenter | #3459 | D3 |
| hypocenter | C3 | C2×#3459 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ #3459 | |
8146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#62892, D3×#62773, D3×#23595, … |
| maximal normal subgroup of | D3×#62892, D3×#62773, D3×#23595, … |
| maximal quotient of | D3×#37744, D3×#52163, D3×#39428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1076311);