Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C172 · Schur multiplier (H2) = C17 |
| direct product | C172×Dic15 |
| unambiguous semidirect product | C3⋊(C172×Dic5) |
| derived, Hall | C3×C5 ⋊ C4×C172 |
| Hall | C3×C5×C172 ⋊ C4 |
| Hall | C5×C172 ⋊ Dic3 |
| Hall | C3×C172 ⋊ Dic5 |
| Sylow | C5 ⋊ Dic3×C172 |
| Sylow | C3 ⋊ C172×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C172 | D15 |
| commutator, hypocenter | C3×C5 | C4×C172 |
| Frattini | C2 | C172×D15 |
| Fitting, socle, prime radical | C2×C3×C5×C172 | C2 |
| cosocle | C2×C3×C5 | C2×C172 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C172 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17340 |
5202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 52);