Finite Group DatabasebetaFinite Group Databasebeta| order | 18693 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×C67⋊C9 |
| unambiguous semidirect product | C67⋊(C9×C31) |
| derived, Sylow | C67 ⋊ C9×C31 |
| Hall | C31×C67 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C31 | C67⋊C3 |
| commutator, hypocenter | C67 | C9×C31 |
| Frattini | C3 | C31×C67⋊C3 |
| Fitting, socle, prime radical | C3×C31×C67 | C3 |
| cosocle | C3×C67 | C3×C31 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C3×C31 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18693 |
2325 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C31×C67⋊C9, C31×D67⋊C9, D31×C67⋊C9, … |
| maximal normal subgroup of | C2×C31×C67⋊C9, C31×D67⋊C9, D31×C67⋊C9, … |
| maximal quotient of | C2×C31×C67⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18693, 3);