Finite Group DatabasebetaFinite Group Databasebeta| order | 6836 |
| automorphism | Aut(G) order 5837944 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1709 |
| derived, Sylow | C1709 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1709 |
| commutator, hypocenter | C1709 | C4 |
| Fitting, socle | C2×C1709 | C2 |
| LCS | G ▷ C1709 | |
| UCS | C1 ◁ C2 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,1709|a^2=b,c^a=c^17081712 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D1709, C2×Dic1709, C22⋊D1709, … |
| maximal normal subgroup of | C4×D1709, C2×Dic1709, C22⋊D1709, … |
| maximal quotient of | #28331805, C2×Dic1709, C3×Dic1709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6836, 1);