Finite Group DatabasebetaFinite Group Databasebeta| order | 6930 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊(D7⋊C9) |
| unambiguous semidirect product | (C7⋊C9)⋊AGL(1,𝔽11) |
| unambiguous semidirect product | (C7⋊AGL(1,𝔽11))⋊C9 |
| unambiguous semidirect product | (C11⋊(D7⋊C9))⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)⋊AGL(1,𝔽11) |
| commutator, hypocenter | C7×C11 | C2×C5×C9 |
| Fitting, socle | C3×C7×C11 | C2×C3×C5 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,7,11,3|b^3=f,d^a=d^6,e^a=e^10,d^b=d^2,e^c=e^4120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6930, 36);