Finite Group DatabasebetaFinite Group Databasebeta| order | 6930 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D1155 |
| unambiguous semidirect product | C5⋊(C3⋊D231) |
| unambiguous semidirect product | C7⋊(C3⋊D165) |
| unambiguous semidirect product | C11⋊(C3⋊D105) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C7×C11 | C2 |
| LCS | G ▷ C32×C5×C7×C11 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,7,11|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^6,f^a=f^101734 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×C3⋊D105, D7×C3⋊D165, C3⋊D15×D77, … |
| maximal normal subgroup of | D11×C3⋊D105, D7×C3⋊D165, C3⋊D15×D77, … |
| maximal quotient of | C3⋊Dic1155, C2×C3⋊D1155, C3⋊D5775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6930, 96);