Finite Group DatabasebetaFinite Group Databasebeta| order | 18662 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D43⋊C7 |
| unambiguous semidirect product | D43⋊(C7×C31) |
| unambiguous semidirect product | (C43⋊C7)⋊(C2×C31) |
| unambiguous semidirect product | (C31×D43)⋊C7 |
| Fitting, socle, Hall | C31×C43 ⋊ C2×C7 |
| derived, Sylow | C43 ⋊ C2×C7×C31 |
| Hall | C31×C43⋊C7 ⋊ C2 |
| Hall | C31×D43 ⋊ C7 |
| Hall | C43⋊C7 ⋊ C2×C31 |
| Hall | D43 ⋊ C7×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D43⋊C7 |
| commutator, cosocle, hypocenter | C43 | C2×C7×C31 |
| Frattini | C1 | G |
| Fitting, socle | C31×C43 | C2×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C31 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1333 |
527 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×D43⋊C7, C2×C31×D43⋊C7 |
| maximal normal subgroup of | D31×D43⋊C7, C2×C31×D43⋊C7 |
| maximal quotient of | C31×Dic43⋊C7, C2×C31×D43⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18662, 10);