Finite Group DatabasebetaFinite Group Databasebeta| order | 17073 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×#14578512 |
| derived, Sylow | C271 ⋊ C7×C9 |
| Hall | C7×C271 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | C271⋊C3 |
| commutator, hypocenter | C271 | C7×C9 |
| Frattini | C3 | C7×C271⋊C3 |
| Fitting, socle, prime radical | C3×C7×C271 | C3 |
| cosocle | C3×C271 | C3×C7 |
| LCS | G ▷ C271 | |
| UCS | C1 ◁ C3×C7 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17073 |
1953 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C7×#14578512, C7×#14578512⋊C2, D7×#14578512, … |
| maximal normal subgroup of | C2×C7×#14578512, C7×#14578512⋊C2, D7×#14578512, … |
| maximal quotient of | C2×C7×#14578512 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17073, 3);