Finite Group DatabasebetaFinite Group Databasebeta| order | 9084 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #15690044⋊C3 |
| Fitting, socle, derived, Sylow | C757 ⋊ C3×C4 |
| Hall | #15690044 ⋊ C3 |
| Hall | C757⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C757 | C3×C4 |
| LCS | G ▷ C757 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,757|a^2=c,d^a=d^87,d^b=d^27,d^c=d^75675 conjugacy classes — view the full character table.
| maximal subgroup of | #41030602, C3×#15690044⋊C3, C3⋊(#15690044⋊C3) |
| maximal normal subgroup of | #41030602, C3×#15690044⋊C3 |
| maximal quotient of | #41030578, C3×#15690044⋊C3, C3⋊(#15690044⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9084, 8);