Finite Group DatabasebetaFinite Group Databasebeta| order | 17514 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C2×C3×#15668589 |
| Fitting, socle | C2×C3×C7×C139 ⋊ C3 |
| derived, Hall | C7×C139 ⋊ C2×C32 |
| Hall | C2×C7×C139 ⋊ C32 |
| Hall | C2×C139 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C139 ⋊ C2×C3×ΓL(1,𝔽8) |
| Hall | C2×C7 ⋊ C3×C139⋊C3 |
| Sylow | C7 ⋊ C2×C3×C139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #15668589 |
| commutator, cosocle, hypocenter | C7×C139 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C139 | C3 |
| LCS | G ▷ C7×C139 | |
| UCS | C1 ◁ C2×C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5838 |
1962 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#26043022, C3×#26043018, C3×#26043014, … |
| maximal normal subgroup of | C3×#26043022, C3×#26043018, C3×#26043014, … |
| maximal quotient of | C3×C4×#15668589, C22×C3×#15668589 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17514, 59);