Finite Group DatabasebetaFinite Group Databasebeta| order | 10710 |
| isoclinism | isoclinic class of C3⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C17 · Schur multiplier (H2) = C3 |
| direct product | C7×C17×C3⋊D15 |
| unambiguous semidirect product | C3⋊(C7×C17×D15) |
| unambiguous semidirect product | C5⋊(C7×C17×C3⋊D3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C17 | C3⋊D15 |
| commutator, cosocle, hypocenter | C32×C5 | C2×C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C17 | C2 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C7×C17 | |
96 conjugacy classes of subgroups.
2856 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×C17×#4380, C7×#15690392, C17×C7⋊#4380, … |
| maximal normal subgroup of | C7×C17×#4380, C7×#15690392, C17×C7⋊#4380, … |
| maximal quotient of | C7×C17×C3⋊Dic15, C2×C7×C17×C3⋊D15 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10710, 45);