Finite Group DatabasebetaFinite Group Databasebeta| order | 6030 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D67⋊C9) |
| unambiguous semidirect product | (C67⋊C9)⋊D5 |
| unambiguous semidirect product | D335⋊C9 |
| derived, Hall | C5×C67 ⋊ C2×C9 |
| Hall | C5×C67⋊C9 ⋊ C2 |
| Hall | D335 ⋊ C9 |
| Hall | C67⋊C9 ⋊ D5 |
| Sylow | C67 ⋊ C9×D5 |
| Sylow | C5 ⋊ D67⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊(D67⋊C3) |
| commutator, hypocenter | C5×C67 | C2×C9 |
| Fitting, socle | C3×C5×C67 | C2×C3 |
| LCS | G ▷ C5×C67 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,67,3|b^3=e,c^a=c^4,d^a=d^66,d^b=d^37201 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D67⋊C9, C2×C5⋊(D67⋊C9), C25⋊(D67⋊C9), … |
| maximal normal subgroup of | D5×D67⋊C9, C2×C5⋊(D67⋊C9), C5×C5⋊(D67⋊C9) |
| maximal quotient of | (C67⋊C9)⋊Dic5, C2×C5⋊(D67⋊C9), C25⋊(D67⋊C9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6030, 12);