Finite Group DatabasebetaFinite Group Databasebeta| order | 16542 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #22552000⋊C2 |
| derived, Sylow | C919 ⋊ C2×C9 |
| Hall | #22552000 ⋊ C2 |
| Hall | D919 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D919⋊C3 |
| commutator, hypocenter | C919 | C2×C9 |
| Fitting, socle, cosocle | C3×C919 | C2×C3 |
| prime radical | C3×D919 | C3 |
| LCS | G ▷ C919 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8271 |
Polycyclic presentation:
2,3,919,3|b^3=d,c^a=c^918,c^b=c^866477 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22552000⋊C2 |
| maximal normal subgroup of | C2×#22552000⋊C2 |
| maximal quotient of | #22552000⋊C4, C2×#22552000⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16542, 2);