Finite Group DatabasebetaFinite Group Databasebeta| order | 10710 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D357 |
| unambiguous semidirect product | C3⋊(C3×C5×D119) |
| unambiguous semidirect product | C17⋊(C3×C5×D21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D357 |
| commutator, cosocle, hypocenter | C3×C7×C17 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C17 | C2 |
| LCS | G ▷ C3×C7×C17 | |
| UCS | C1 ◁ C3×C5 | |
72 conjugacy classes of subgroups.
2700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D17×D21, C3×C5×D7×D51, C3×C5×D3×D119, … |
| maximal normal subgroup of | C3×C5×D17×D21, C3×C5×D7×D51, C3×C5×D3×D119, … |
| maximal quotient of | C3×C5×Dic357, C2×C3×C5×D357 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10710, 54);