Finite Group DatabasebetaFinite Group Databasebeta| order | 18354 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1311 |
| unambiguous semidirect product | C3⋊(C7×D437) |
| unambiguous semidirect product | C19⋊(C7×D69) |
| unambiguous semidirect product | C23⋊(C7×D57) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1311 |
| commutator, cosocle, hypocenter | C3×C19×C23 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C19×C23 | C2 |
| LCS | G ▷ C3×C19×C23 | |
| UCS | C1 ◁ C7 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9177 |
4599 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D23×D57, C7×D19×D69, D3×C7×D437, … |
| maximal normal subgroup of | C7×D23×D57, C7×D19×D69, D3×C7×D437, … |
| maximal quotient of | C7×Dic1311, C2×C7×D1311 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18354, 16);