Finite Group DatabasebetaFinite Group Databasebeta| order | 1364 |
| isoclinism | isoclinic class of D11×D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D31 |
| unambiguous semidirect product | (D11×C31)⋊C2 |
| unambiguous semidirect product | (C11×D31)⋊C2 |
| unambiguous semidirect product | D341⋊C2 |
| Fitting, socle, derived, Hall | C11×C31 ⋊ C22 |
| Sylow | C31 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C31 | C22 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 42 |
| transitive degree | μt(G) = 341 |
119 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D31⋊C3, C3×D11×D31, D31×D33, … |
| maximal normal subgroup of | D11×D31⋊C3, C3×D11×D31, C11×D11×D31, … |
| maximal quotient of | C3×D11×D31, D31×D33, D11×D93, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1364, 5);