Finite Group DatabasebetaFinite Group Databasebeta| order | 18018 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×D231 |
| unambiguous semidirect product | C3⋊(C13⋊C3×D77) |
| unambiguous semidirect product | C11⋊(C13⋊C3×D21) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C11×C13 | C2×C3 |
| LCS | G ▷ C3×C7×C11×C13 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3003 |
819 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13⋊C3×D231, (C11⋊(D13⋊C3))⋊D21, D11×C13⋊C3×D21, … |
| maximal normal subgroup of | D13⋊C3×D231, (C11⋊(D13⋊C3))⋊D21, D11×C13⋊C3×D21, … |
| maximal quotient of | C13⋊C3×Dic231, C2×C13⋊C3×D231 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18018, 117);