Finite Group DatabasebetaFinite Group Databasebeta| order | 6980 |
| automorphism | Aut(G) order 4858080 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1745 |
| derived, Hall | C5×C349 ⋊ C4 |
| Sylow | C349 ⋊ Dic5 |
| Sylow | C5 ⋊ Dic349 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1745 |
| commutator, hypocenter | C5×C349 | C4 |
| Fitting, socle | C2×C5×C349 | C2 |
| LCS | G ▷ C5×C349 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,349,2|a^2=d,b^a=b^4,c^a=c^3481748 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic1745, Dic5235, Dic1745⋊C3, … |
| maximal normal subgroup of | C3×Dic1745, Dic1745⋊C3, C5×Dic1745, … |
| maximal quotient of | C3×Dic1745, Dic5235, Dic8725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6980, 4);