Finite Group DatabasebetaFinite Group Databasebeta| order | 16542 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#22552000 |
| derived, Sylow | C919 ⋊ C2×C9 |
| Hall | C2×C919 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C919⋊C3 |
| commutator, hypocenter | C919 | C2×C9 |
| Frattini | C3 | C2×C919⋊C3 |
| Fitting, socle, prime radical | C2×C3×C919 | C3 |
| cosocle | C3×C919 | C2×C3 |
| LCS | G ▷ C919 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16542 |
1854 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #22552000⋊C4, C4×#22552000, C2×#22552000⋊C2, … |
| maximal normal subgroup of | #22552000⋊C4, C4×#22552000, C2×#22552000⋊C2, … |
| maximal quotient of | C4×#22552000, C22×#22552000 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16542, 3);