Finite Group DatabasebetaFinite Group Databasebeta| order | 16926 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D273 |
| unambiguous semidirect product | C3⋊(C31×D91) |
| unambiguous semidirect product | C7⋊(C31×D39) |
| unambiguous semidirect product | C13⋊(C31×D21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D273 |
| commutator, cosocle, hypocenter | C3×C7×C13 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13×C31 | C2 |
| LCS | G ▷ C3×C7×C13 | |
| UCS | C1 ◁ C31 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8463 |
4278 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×D273, D13×C31×D21, D403⋊D21, … |
| maximal normal subgroup of | D31×D273, D13×C31×D21, D403⋊D21, … |
| maximal quotient of | C31×Dic273, C2×C31×D273 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16926, 28);