Finite Group DatabasebetaFinite Group Databasebeta| order | 18102 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×D431 |
| unambiguous semidirect product | C431⋊(C2×C3×C7) |
| Fitting, socle, Hall | C3×C7×C431 ⋊ C2 |
| derived, Sylow | C431 ⋊ C2×C3×C7 |
| Hall | C7×C431 ⋊ C2×C3 |
| Hall | C3×C431 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | D431 |
| commutator, cosocle, hypocenter | C431 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C431 | C2 |
| LCS | G ▷ C431 | |
| UCS | C1 ◁ C3×C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9051 |
4557 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D7×D431, D3×C7×D431, D21×D431, … |
| maximal normal subgroup of | C3×D7×D431, D3×C7×D431, D21×D431, … |
| maximal quotient of | C3×C7×Dic431, C2×C3×C7×D431 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18102, 3);