Finite Group DatabasebetaFinite Group Databasebeta| order | 7068 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic589 |
| derived, Hall | C19×C31 ⋊ C3×C4 |
| Hall | C3×C19×C31 ⋊ C4 |
| Hall | C3×C31 ⋊ Dic19 |
| Hall | C3×C19 ⋊ Dic31 |
| Sylow | C31 ⋊ C3×Dic19 |
| Sylow | C19 ⋊ C3×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D589 |
| commutator, hypocenter | C19×C31 | C3×C4 |
| Frattini | C2 | C3×D589 |
| Fitting, socle | C2×C3×C19×C31 | C2 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
1776 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×Dic589, (C31⋊C9)⋊Dic19, #4294⋊Dic31, … |
| maximal normal subgroup of | C9×Dic589, (C31⋊C9)⋊Dic19, #4294⋊Dic31, … |
| maximal quotient of | C9×Dic589, C3×Dic1767, C32×Dic589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7068, 8);