Finite Group DatabasebetaFinite Group Databasebeta| order | 9860 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C5×C17×#1181 |
| Fitting, socle, Hall | C5×C17×C29 ⋊ C4 |
| derived, Sylow | C29 ⋊ C4×C5×C17 |
| Hall | C17×C29 ⋊ C4×C5 |
| Hall | C5×C29 ⋊ C4×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C17 | #1181 |
| commutator, hypocenter | C29 | C4×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C29 | C4 |
| prime radical | C5×C17×D29 | C2 |
| cosocle | D29 | C2×C5×C17 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C5×C17 | |
24 conjugacy classes of subgroups.
935 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×C17×#1181, C5×C17×C3⋊#1181 |
| maximal normal subgroup of | C3×C5×C17×#1181 |
| maximal quotient of | C3×C5×C17×#1181, C5×C17×C3⋊#1181 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9860, 10);