Finite Group DatabasebetaFinite Group Databasebeta| order | 10170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D565 |
| unambiguous semidirect product | C5⋊(C32×D113) |
| unambiguous semidirect product | C113⋊(C32×D5) |
| Fitting, socle, Hall | C32×C5×C113 ⋊ C2 |
| derived, Hall | C5×C113 ⋊ C2×C32 |
| Hall | C32×C113 ⋊ D5 |
| Sylow | C113 ⋊ C32×D5 |
| Hall | C32×C5 ⋊ D113 |
| Sylow | C5 ⋊ C32×D113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D565 |
| commutator, cosocle, hypocenter | C5×C113 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C113 | C2 |
| LCS | G ▷ C5×C113 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
2556 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×#14555933, C32×#14555934, C32×D5×D113, … |
| maximal normal subgroup of | C32×#14555933, C32×#14555934, C32×D5×D113, … |
| maximal quotient of | C32×Dic565, C2×C32×D565 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10170, 18);