Finite Group DatabasebetaFinite Group Databasebeta| order | 744 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C1 |
| direct product | Dic6×C31 |
| unambiguous semidirect product | C3⋊(Q8×C31) |
| Hall | C3×C31 ⋊ Q8 |
| Sylow | C3 ⋊ Q8×C31 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 744 |
279 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13093436, #13093441, #13093442, … |
| maximal normal subgroup of | #13093436, #13093441, #13093442, … |
| maximal quotient of | C31×Dic3⋊C4, C31×C4⋊Dic3, C2×Dic6×C31 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(744, 29);