Finite Group DatabasebetaFinite Group Databasebeta| order | 17514 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#19154246 |
| Fitting, socle | C3×C7×C139 ⋊ C2×C3 |
| derived, Hall | C7×C139 ⋊ C2×C32 |
| Hall | C3×#15668588 ⋊ C2 |
| Hall | C7×D139 ⋊ C32 |
| Hall | D139 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C139 ⋊ C2×C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×D139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #19154246 |
| commutator, cosocle, hypocenter | C7×C139 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C139 | C2×C3 |
| LCS | G ▷ C7×C139 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2919 |
513 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#19154246⋊C2, #19154246⋊D3, D3×#19154246, … |
| maximal normal subgroup of | C3×#19154246⋊C2, #19154246⋊D3, D3×#19154246, … |
| maximal quotient of | C3×#26043015, C2×C3×#19154246 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17514, 37);