Finite Group DatabasebetaFinite Group Databasebeta| order | 17670 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19×C31 · Schur multiplier (H2) = C1 |
| direct product | C19×D15×C31 |
| unambiguous semidirect product | C3⋊(D5×C19×C31) |
| unambiguous semidirect product | C5⋊(D3×C19×C31) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19×C31 | D15 |
| commutator, cosocle, hypocenter | C3×C5 | C2×C19×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C19×C31 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C19×C31 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8835 |
5301 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×D15×D31, D15×C31×D19, D15×D589, … |
| maximal normal subgroup of | C19×D15×D31, D15×C31×D19, D15×D589, … |
| maximal quotient of | C19×C31×Dic15, C2×C19×D15×C31 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17670, 22);