Finite Group DatabasebetaFinite Group Databasebeta| order | 17574 |
| isoclinism | isoclinic class of D87 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C101 · Schur multiplier (H2) = C1 |
| direct product | C101×D87 |
| unambiguous semidirect product | C3⋊(D29×C101) |
| unambiguous semidirect product | C29⋊(D3×C101) |
| Fitting, socle, Hall | C3×C29×C101 ⋊ C2 |
| derived, Hall | C3×C29 ⋊ C2×C101 |
| Hall | C29×C101 ⋊ D3 |
| Hall | C3×C101 ⋊ D29 |
| Sylow | C29 ⋊ D3×C101 |
| Sylow | C3 ⋊ D29×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C101 | D87 |
| commutator, cosocle, hypocenter | C3×C29 | C2×C101 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C101 | C2 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C101 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8787 |
4545 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D87×D101, D3×D29×C101, D87⋊D101, … |
| maximal normal subgroup of | D87×D101, D3×D29×C101, D87⋊D101, … |
| maximal quotient of | C101×Dic87, C2×C101×D87 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17574, 7);