Finite Group DatabasebetaFinite Group Databasebeta| order | 10710 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7×C17 · Schur multiplier (H2) = C3 |
| direct product | C5×C7×C17×C3⋊D3 |
| unambiguous semidirect product | C3⋊(C5×D3×C7×C17) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7×C17 | C3⋊D3 |
| commutator, cosocle, hypocenter | C32 | C2×C5×C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C17 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C5×C7×C17 | |
96 conjugacy classes of subgroups.
3570 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10710, 49);