Finite Group DatabasebetaFinite Group Databasebeta| order | 10602 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#16812967 |
| Fitting, socle | C3×C19×C31 ⋊ C2×C3 |
| derived, Hall | C19×C31 ⋊ C2×C32 |
| Hall | C3×#13183715 ⋊ C2 |
| Hall | C19×D31 ⋊ C32 |
| Hall | D31 ⋊ C3×C19⋊C3 |
| Sylow | C31 ⋊ C2×C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×D31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16812967 |
| commutator, cosocle, hypocenter | C19×C31 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C31 | C2×C3 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
339 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#16812967⋊C2, #16812967⋊D3, D3×#16812967, … |
| maximal normal subgroup of | C3×#16812967⋊C2, #16812967⋊D3, D3×#16812967, … |
| maximal quotient of | C3×#20296611, C2×C3×#16812967 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10602, 50);