Finite Group DatabasebetaFinite Group Databasebeta| order | 10370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D305 |
| unambiguous semidirect product | C5⋊(C17×D61) |
| unambiguous semidirect product | C61⋊(D5×C17) |
| Fitting, socle, Hall | C5×C17×C61 ⋊ C2 |
| derived, Hall | C5×C61 ⋊ C2×C17 |
| Hall | C17×C61 ⋊ D5 |
| Hall | C5×C17 ⋊ D61 |
| Sylow | C61 ⋊ D5×C17 |
| Sylow | C5 ⋊ C17×D61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D305 |
| commutator, cosocle, hypocenter | C5×C61 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C61 | C2 |
| LCS | G ▷ C5×C61 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
2618 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×#11927412, C17×#11927413, #35208711, … |
| maximal normal subgroup of | C17×#11927412, C17×#11927413, #35208711, … |
| maximal quotient of | C17×Dic305, C2×C17×D305, C3×C17×D305, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10370, 7);