Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #15690146⋊C2 |
| derived, Hall | #13095201 ⋊ C22 |
| Sylow | C132 ⋊ C2×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | #13095201 | C22 |
| Frattini | C3 | #11759813⋊C2 |
| Fitting, socle | C3×C132 | C2×D3 |
| LCS | G ▷ #13095201 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,13^2,3|c^3=f^2,d^a=d^12,e^a=e^12,c^b=c^2f,d^b=e^4,e^b=d^10,f^b=f^2,d^c=d^9,e^c=e^372 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#15690146⋊C2, #15690146⋊D5, #44477698 |
| maximal normal subgroup of | C5×#15690146⋊C2 |
| maximal quotient of | C5×#15690146⋊C2, #15690146⋊D5, #44477698 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 91);