Finite Group DatabasebetaFinite Group Databasebeta| order | 16698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C121 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D23⋊C121) |
| unambiguous semidirect product | D69⋊C121 |
| unambiguous semidirect product | (C23⋊C121)⋊D3 |
| derived, Hall | C3×C23 ⋊ C2×C121 |
| Hall | C3×C23⋊C121 ⋊ C2 |
| Hall | C23⋊C121 ⋊ D3 |
| Hall | D69 ⋊ C121 |
| Sylow | C23 ⋊ D3×C121 |
| Sylow | C3 ⋊ D23⋊C121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C11 | C3⋊AGL(1,𝔽23) |
| commutator, hypocenter | C3×C23 | C2×C121 |
| Fitting, socle, cosocle | C3×C11×C23 | C2×C11 |
| prime radical | C11×D69 | C11 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8349 |
Polycyclic presentation:
2,11,3,23,11|b^11=e,c^a=c^2,d^a=d^22,d^b=d^3396 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D23⋊C121, C2×C3⋊(D23⋊C121) |
| maximal normal subgroup of | D3×D23⋊C121, C2×C3⋊(D23⋊C121) |
| maximal quotient of | C3⋊(Dic23⋊C121), C2×C3⋊(D23⋊C121) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16698, 4);