Finite Group DatabasebetaFinite Group Databasebeta| order | 1386 |
| isoclinism | isoclinic class of C11⋊AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(D7⋊C9) |
| unambiguous semidirect product | (C7⋊C9)⋊D11 |
| unambiguous semidirect product | D77⋊C9 |
| derived, Hall | C7×C11 ⋊ C2×C9 |
| Hall | C11×C7⋊C9 ⋊ C2 |
| Hall | D77 ⋊ C9 |
| Hall | C7⋊C9 ⋊ D11 |
| Sylow | C11 ⋊ D7⋊C9 |
| Sylow | C7 ⋊ C9×D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C11⋊AGL(1,𝔽7) |
| commutator, hypocenter | C7×C11 | C2×C9 |
| Fitting, socle, cosocle | C3×C7×C11 | C2×C3 |
| prime radical | C3×D77 | C3 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 693 |
Polycyclic presentation:
2,3^2,7,11|b^3=c,d^a=d^6,e^a=e^10,d^b=d^496 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D7⋊C9, C2×C11⋊(D7⋊C9), (C7⋊C9)⋊D121, … |
| maximal normal subgroup of | D11×D7⋊C9, C2×C11⋊(D7⋊C9), C11×C11⋊(D7⋊C9), … |
| maximal quotient of | C11⋊(Dic7⋊C9), C2×C11⋊(D7⋊C9), (C7⋊C9)⋊D121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1386, 3);