Finite Group DatabasebetaFinite Group Databasebeta| order | 18018 |
| isoclinism | isoclinic class of C3⋊D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C3 |
| direct product | C7×C11×C3⋊D39 |
| unambiguous semidirect product | C3⋊(C7×C11×D39) |
| unambiguous semidirect product | C13⋊(C7×C11×C3⋊D3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C11 | C3⋊D39 |
| commutator, cosocle, hypocenter | C32×C13 | C2×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C11×C13 | C2 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 ◁ C7×C11 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9009 |
4620 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×C11×#90866, C7×C11⋊#90866, C11×C7⋊#90866, … |
| maximal normal subgroup of | C7×C11×#90866, C7×C11⋊#90866, C11×C7⋊#90866, … |
| maximal quotient of | C7×C11×C3⋊Dic39, C2×C7×C11×C3⋊D39 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18018, 128);