Finite Group DatabasebetaFinite Group Databasebeta| order | 16665 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×#19149920 |
| Fitting, socle, Hall | C3×C11×C101 ⋊ C5 |
| derived, Hall | C11×C101 ⋊ C3×C5 |
| Hall | C3×C101 ⋊ C11⋊C5 |
| Sylow | C101 ⋊ C3×C11⋊C5 |
| Hall | C3×C11 ⋊ C101⋊C5 |
| Sylow | C11 ⋊ C3×C101⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #19149920 |
| commutator, cosocle, hypocenter | C11×C101 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C101 | C5 |
| LCS | G ▷ C11×C101 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3333 |
681 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×#19149920, C3×#26013193, C3×#26013199, … |
| maximal normal subgroup of | C2×C3×#19149920, C3×#26013193, C3×#26013199, … |
| maximal quotient of | C2×C3×#19149920 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16665, 7);