Finite Group DatabasebetaFinite Group Databasebeta| order | 18018 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C3⋊#10587717 |
| unambiguous semidirect product | C3⋊(C11×#10587717) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊#10587717 |
| commutator, cosocle, hypocenter | C3×C7×C13 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C11×C13 | C2×C3 |
| LCS | G ▷ C3×C7×C13 | |
| UCS | C1 ◁ C11 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3003 |
627 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#10587721⋊D3, C11×#10587723⋊D3, #49114738, … |
| maximal normal subgroup of | C11×#10587721⋊D3, C11×#10587723⋊D3, #49114738, … |
| maximal quotient of | C11×C3⋊#11763958, C2×C11×C3⋊#10587717 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18018, 104);