Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C132 ⋊ C22 |
| Sylow | C132 ⋊ C2×C3⋊D3 |
| Sylow | C32 ⋊ D132 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C132 | C22 |
| LCS | G ▷ C32×C132 | |
| UCS | C1 | |
192 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,13^2|c^a=c^2,d^a=d^2,e^a=e^12,e^b=e^12,f^b=f^12408 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#20258962, #44478316, #44478326 |
| maximal normal subgroup of | C5×#20258962 |
| maximal quotient of | C5×#20258962, #44478316, #44478326 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 269);