Finite Group DatabasebetaFinite Group Databasebeta| order | 6836 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C1709 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1709 | C4 |
| LCS | G ▷ C1709 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,1709|a^2=b,c^a=c^390,c^b=c^1708431 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20292020, C3×#20292020, C3⋊#20292020, … |
| maximal normal subgroup of | C2×#20292020, C3×#20292020, C5×#20292020 |
| maximal quotient of | #28331812, C2×#20292020, C3×#20292020, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6836, 3);