Finite Group DatabasebetaFinite Group Databasebeta| order | 9006 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C79 ⋊ C2×C3 |
| Hall | #17985164 ⋊ C2 |
| Hall | D19×C79 ⋊ C3 |
| Sylow | C79 ⋊ D19⋊C3 |
| Hall | D19 ⋊ C79⋊C3 |
| Sylow | C19 ⋊ C2×C79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C79 | C2×C3 |
| LCS | G ▷ C19×C79 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,19,79|c^a=c^18,c^b=c^7,d^b=d^55295 conjugacy classes — view the full character table.
| maximal subgroup of | #22583034⋊C2, C2×#22583038, D19⋊C3×C79⋊C3, … |
| maximal normal subgroup of | #22583034⋊C2, C2×#22583038, D19⋊C3×C79⋊C3, … |
| maximal quotient of | #31824708, C2×#22583038, #41028270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9006, 20);