Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C13 · Schur multiplier (H2) = C2×C3 |
| direct product | C22×C3×C13×C13⋊C3 |
| Fitting, socle | C22×C3×C132 ⋊ C3 |
| derived | C13 ⋊ C22×C32×C13 |
| Hall | C22×C132 ⋊ C32 |
| Sylow | C132 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C13 | C13⋊C3 |
| commutator, hypocenter | C13 | C22×C32×C13 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C132 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C3×C13 | |
160 conjugacy classes of subgroups.
1092 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×D5×C13×C13⋊C3, C22×C3×C5×C13×C13⋊C3 |
| maximal normal subgroup of | C22×C3×C5×C13×C13⋊C3 |
| maximal quotient of | C2×C3×D5×C13×C13⋊C3, C22×C3×C5×C13×C13⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 289);