Finite Group DatabasebetaFinite Group Databasebeta| order | 10370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D17×C61⋊C5 |
| unambiguous semidirect product | C17⋊(C2×C61⋊C5) |
| unambiguous semidirect product | (D17×C61)⋊C5 |
| Fitting, socle, derived, Hall | C17×C61 ⋊ C2×C5 |
| Hall | C17×C61⋊C5 ⋊ C2 |
| Hall | D17×C61 ⋊ C5 |
| Sylow | C61 ⋊ C5×D17 |
| Sylow | C17 ⋊ C2×C61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C61 | C2×C5 |
| LCS | G ▷ C17×C61 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
170 conjugacy classes — view the full character table.
| maximal subgroup of | #16861897⋊C5, #595×C61⋊C5, D17×D61⋊C5, … |
| maximal normal subgroup of | #16861897⋊C5, #595×C61⋊C5, D17×D61⋊C5, … |
| maximal quotient of | Dic17×C61⋊C5, C2×D17×C61⋊C5, C3×D17×C61⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10370, 11);