Finite Group DatabasebetaFinite Group Databasebeta| order | 10370 |
| automorphism | Aut(G) order 19910400 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5185 |
| unambiguous semidirect product | C5⋊D1037 |
| unambiguous semidirect product | C17⋊D305 |
| unambiguous semidirect product | C61⋊D85 |
| Fitting, socle, derived, Hall | C5×C17×C61 ⋊ C2 |
| Hall | C17×C61 ⋊ D5 |
| Hall | C5×C61 ⋊ D17 |
| Hall | C5×C17 ⋊ D61 |
| Sylow | C61 ⋊ D85 |
| Sylow | C17 ⋊ D305 |
| Sylow | C5 ⋊ D1037 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C17×C61 | C2 |
| LCS | G ▷ C5×C17×C61 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,17,61|b^a=b^4,c^a=c^16,d^a=d^602594 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35208703, #35208704, #35208707, … |
| maximal normal subgroup of | #35208703, #35208704, #35208707, … |
| maximal quotient of | Dic5185, C2×D5185, C3×D5185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10370, 9);