Finite Group DatabasebetaFinite Group Databasebeta| order | 17514 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C7⋊C9×D139 |
| derived, Hall | C7×C139 ⋊ C2×C9 |
| Hall | C7⋊C9×C139 ⋊ C2 |
| Hall | C7×D139 ⋊ C9 |
| Sylow | C139 ⋊ C2×C7⋊C9 |
| Sylow | C7 ⋊ C9×D139 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)×D139 |
| commutator, hypocenter | C7×C139 | C2×C9 |
| Fitting, socle, cosocle | C3×C7×C139 | C2×C3 |
| prime radical | C3×C7×D139 | C3 |
| LCS | G ▷ C7×C139 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8757 |
1065 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7⋊C9×D139, C2×C7⋊C9×D139 |
| maximal normal subgroup of | D7⋊C9×D139, C2×C7⋊C9×D139 |
| maximal quotient of | C7⋊C9×Dic139, C2×C7⋊C9×D139 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17514, 14);