Finite Group DatabasebetaFinite Group Databasebeta| order | 10370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(D61⋊C5) |
| unambiguous semidirect product | (C61⋊C5)⋊D17 |
| unambiguous semidirect product | D1037⋊C5 |
| Fitting, socle, derived, Hall | C17×C61 ⋊ C2×C5 |
| Hall | C17×C61⋊C5 ⋊ C2 |
| Hall | D1037 ⋊ C5 |
| Hall | C61⋊C5 ⋊ D17 |
| Sylow | C61 ⋊ C5×D17 |
| Sylow | C17 ⋊ D61⋊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.
Polycyclic presentation:
2,5,17,61|c^a=c^16,d^a=d^60,d^b=d^9152 conjugacy classes — view the full character table.
| maximal subgroup of | #16861895⋊C5, #16861896⋊C5, D17×D61⋊C5, … |
| maximal normal subgroup of | #16861895⋊C5, #16861896⋊C5, D17×D61⋊C5, … |
| maximal quotient of | Dic1037⋊C5, C2×C17⋊(D61⋊C5), C3×C17⋊(D61⋊C5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10370, 12);