Finite Group DatabasebetaFinite Group Databasebeta| order | 6108 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#14523266 |
| Fitting, socle, derived, Hall | C3×C509 ⋊ C4 |
| Sylow | C509 ⋊ Dic3 |
| Sylow | C3 ⋊ #14523266 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C509 | C4 |
| LCS | G ▷ C3×C509 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,509|a^2=b,c^a=c^2,d^a=d^208,d^b=d^508387 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#14523266, C3×C3⋊#14523266, C3⋊(C3⋊#14523266), … |
| maximal normal subgroup of | C3×C3⋊#14523266, C5×C3⋊#14523266 |
| maximal quotient of | C9⋊#14523266, C3×C3⋊#14523266, C3⋊(C3⋊#14523266), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6108, 7);