Finite Group DatabasebetaFinite Group Databasebeta| order | 17238 |
| isoclinism | isoclinic class of C13⋊D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C13 |
| direct product | C3×C17×C13⋊D13 |
| Fitting, socle, Hall | C3×C132×C17 ⋊ C2 |
| derived, Sylow | C132 ⋊ C2×C3×C17 |
| Hall | C132×C17 ⋊ C2×C3 |
| Hall | C3×C132 ⋊ C2×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | C13⋊D13 |
| commutator, cosocle, hypocenter | C132 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C132×C17 | C2 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C3×C17 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8619 |
4386 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C17×D132, C3×(C13⋊D13)⋊D17, C3×D17×C13⋊D13, … |
| maximal normal subgroup of | C3×C17×D132, C3×(C13⋊D13)⋊D17, C3×D17×C13⋊D13, … |
| maximal quotient of | C3×C17×#10621725, C2×C3×C17×C13⋊D13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17238, 43);