Finite Group DatabasebetaFinite Group Databasebeta| order | 1364 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C11×D31 |
| unambiguous semidirect product | C31⋊(C22×C11) |
| unambiguous semidirect product | (C2×C31)⋊(C2×C11) |
| Fitting, socle | C2×C11×C31 ⋊ C2 |
| derived, Sylow | C31 ⋊ C22×C11 |
| Hall | C11×C31 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D31 |
| commutator, cosocle, hypocenter | C31 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C31 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C11 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 682 |
374 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11×D31⋊C3, D3×C11×D31, C2×C3×C11×D31, … |
| maximal normal subgroup of | C2×C11×D31⋊C3, C2×C3×C11×D31, C2×D31×C121, … |
| maximal quotient of | D3×C11×D31, C2×C3×C11×D31, C2×C11×D93, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1364, 6);