Finite Group DatabasebetaFinite Group Databasebeta| order | 10756 |
| automorphism | Aut(G) order 14456064 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2689 |
| derived, Sylow | C2689 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2689 |
| commutator, hypocenter | C2689 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C2689 | C2 |
| LCS | G ▷ C2689 | |
| UCS | C1 ◁ C2 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,2689|a^2=b,c^a=c^26882692 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D2689, C2×Dic2689, C22⋊D2689, … |
| maximal normal subgroup of | C4×D2689, C2×Dic2689, C22⋊D2689, … |
| maximal quotient of | #36340185, C2×Dic2689, C3×Dic2689, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10756, 1);