Finite Group DatabasebetaFinite Group Databasebeta| order | 1364 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | C2×D11×C31 |
| unambiguous semidirect product | C11⋊(C22×C31) |
| unambiguous semidirect product | (C2×C11)⋊(C2×C31) |
| Fitting, socle | C2×C11×C31 ⋊ C2 |
| derived, Sylow | C11 ⋊ C22×C31 |
| Hall | C11×C31 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | D11 |
| commutator, cosocle, hypocenter | C11 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C31 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C31 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 682 |
434 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D11×C31⋊C3, D3×D11×C31, C2×C3×D11×C31, … |
| maximal normal subgroup of | C2×D11×C31⋊C3, C2×C3×D11×C31, C2×C11×D11×C31, … |
| maximal quotient of | D3×D11×C31, C2×C3×D11×C31, C2×C31×D33, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1364, 7);