Finite Group DatabasebetaFinite Group Databasebeta| order | 6030 |
| isoclinism | isoclinic class of D67⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C5×C67 ⋊ C2×C3 |
| derived, Sylow | C67 ⋊ C2×C32×C5 |
| Hall | C3×C5×C67⋊C3 ⋊ C2 |
| Hall | C5×D67 ⋊ C32 |
| Hall | C3×C67⋊C3 ⋊ C2×C5 |
| Hall | C5×C67 ⋊ C2×C32 |
| Hall | D67 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D67⋊C3 |
| commutator, hypocenter | C67 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C67 | C2×C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C3×C5 | |
48 conjugacy classes of subgroups.
255 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×D67⋊C3, C5×D3×D67⋊C3, D15×D67⋊C3, … |
| maximal normal subgroup of | C3×D5×D67⋊C3, C5×D3×D67⋊C3, D15×D67⋊C3, … |
| maximal quotient of | C3×C5×(C67⋊C3)⋊C4, C2×C3×C5×D67⋊C3, C3×C25×D67⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6030, 14);