Finite Group DatabasebetaFinite Group Databasebeta| order | 10676 |
| automorphism | Aut(G) order 13323648 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2669 |
| derived, Hall | C17×C157 ⋊ C4 |
| Sylow | C157 ⋊ Dic17 |
| Sylow | C17 ⋊ Dic157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2669 |
| commutator, hypocenter | C17×C157 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C17×C157 | C2 |
| LCS | G ▷ C17×C157 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,17,157,2|a^2=d,b^a=b^16,c^a=c^1562672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2669, Dic8007, Dic2669⋊C3, … |
| maximal normal subgroup of | C3×Dic2669, Dic2669⋊C3, Dic5338 |
| maximal quotient of | C3×Dic2669, Dic8007, Dic13345 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10676, 4);