Finite Group DatabasebetaFinite Group Databasebeta| order | 870 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C29 · Schur multiplier (H2) = C1 |
| direct product | C5×D3×C29 |
| unambiguous semidirect product | C3⋊(C2×C5×C29) |
| Fitting, socle, Hall | C3×C5×C29 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C5×C29 |
| Hall | C3×C29 ⋊ C2×C5 |
| Hall | C3×C5 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C29 | D3 |
| commutator, cosocle, hypocenter | C3 | C2×C5×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C29 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C5×C29 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 435 |
435 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D29, D3×D5×C29, D3×D145, … |
| maximal normal subgroup of | C5×D3×D29, D3×D5×C29, D3×D145, … |
| maximal quotient of | C5×Dic3×C29, C2×C5×D3×C29, C5×D9×C29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(870, 4);