Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C132 ⋊ C4×C9 |
| Hall | #13095200 ⋊ C4 |
| Hall | #10621730 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #14523148 |
| commutator, hypocenter | C132 | C4×C9 |
| Fitting, socle | C3×C132 | C3×C4 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C3 | |
45 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,13^2,3|a^2=c,b^3=f,d^a=d^5,e^a=e^12,d^b=d^3,e^b=e^3,d^c=d^1287 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#20258772, #44477641, #44477642, … |
| maximal normal subgroup of | C5×#20258772 |
| maximal quotient of | C5×#20258772, #44477641, #44477642, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 79);