Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D117⋊D13 |
| Fitting, derived, Hall | C9×C132 ⋊ C22 |
| Sylow | C132 ⋊ C2×D9 |
| Sylow | C9 ⋊ D132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C132 | C22 |
| Frattini | C3 | D39⋊D13 |
| socle | C3×C132 | C2×D3 |
| LCS | G ▷ C9×C132 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,13^2,3|c^3=f^2,c^a=c^2f,d^a=d^12,f^a=f^2,d^b=d^12,e^b=e^12408 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D117⋊D13, #44477768, D117⋊D65 |
| maximal normal subgroup of | C5×D117⋊D13 |
| maximal quotient of | C5×D117⋊D13, #44477768, D117⋊D65 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 113);