Finite Group DatabasebetaFinite Group Databasebeta| order | 16542 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#22552002 |
| Fitting, socle, Hall | C2×C919 ⋊ C9 |
| derived, Sylow | C919 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #22552002 |
| commutator, hypocenter | C919 | C2×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C919 | C9 |
| prime radical | C2×C919⋊C3 | C3 |
| cosocle | C919⋊C3 | C2×C3 |
| LCS | G ▷ C919 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1838 |
222 conjugacy classes — view the full character table.
| maximal subgroup of | #22552002⋊C4, C4×#22552002, C2×#22552002⋊C2, … |
| maximal normal subgroup of | #22552002⋊C4, C4×#22552002, C2×#22552002⋊C2, … |
| maximal quotient of | C4×#22552002, C22×#22552002 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16542, 9);