Finite Group DatabasebetaFinite Group Databasebeta| order | 17670 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D285 |
| unambiguous semidirect product | C3⋊(C31×D95) |
| unambiguous semidirect product | C5⋊(C31×D57) |
| unambiguous semidirect product | C19⋊(D15×C31) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D285 |
| commutator, cosocle, hypocenter | C3×C5×C19 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C19×C31 | C2 |
| LCS | G ▷ C3×C5×C19 | |
| UCS | C1 ◁ C31 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8835 |
4464 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×D285, D15×C31×D19, D589⋊D15, … |
| maximal normal subgroup of | D31×D285, D15×C31×D19, D589⋊D15, … |
| maximal quotient of | C31×Dic285, C2×C31×D285 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17670, 24);