Finite Group DatabasebetaFinite Group Databasebeta| order | 10710 |
| isoclinism | isoclinic class of D153 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×D153 |
| unambiguous semidirect product | C9⋊(C5×C7×D17) |
| unambiguous semidirect product | C17⋊(C5×C7×D9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | D153 |
| commutator, cosocle, hypocenter | C9×C17 | C2×C5×C7 |
| Frattini | C3 | C5×C7×D51 |
| Fitting | C5×C7×C9×C17 | C2 |
| socle | C3×C5×C7×C17 | D3 |
| LCS | G ▷ C9×C17 | |
| UCS | C1 ◁ C5×C7 | |
48 conjugacy classes of subgroups.
2730 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×D9×D17, C5×D7×D153, C5×D63⋊D17, … |
| maximal normal subgroup of | C5×C7×D9×D17, C5×D7×D153, C5×D63⋊D17, … |
| maximal quotient of | C5×C7×Dic153, C2×C5×C7×D153 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10710, 11);