Finite Group DatabasebetaFinite Group Databasebeta| order | 744 |
| isoclinism | isoclinic class of A4×D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | A4×D31 |
| Fitting, socle, derived | C22×C31 ⋊ C2×C3 |
| Hall | C22×D31 ⋊ C3 |
| Sylow | C31 ⋊ C2×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C31 | C2×C3 |
| LCS | G ▷ C22×C31 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 124 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | S4×D31, C2×A4×D31, A4×D31⋊C5, … |
| maximal normal subgroup of | S4×D31, C2×A4×D31, A4×D31⋊C5, … |
| maximal quotient of | #13093534, SL(2,𝔽3)×D31, A4×Dic31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(744, 45);