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 | C13×Dic13 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | #11759817 |
| commutator, hypocenter | C132 | C4×C9 |
| Fitting, socle | C2×C3×C132 | C2×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C2×C3 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13^2,2,3|a^2=e,b^3=f,c^a=c^12,c^b=c^9,d^b=d^9240 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#20258754, #44477590, #44477659 |
| maximal normal subgroup of | C5×#20258754 |
| maximal quotient of | C5×#20258754, #44477590, #44477659 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 61);