Finite Group DatabasebetaFinite Group Databasebeta| order | 8636 |
| automorphism | Aut(G) order 8705088 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2159 |
| unambiguous semidirect product | C127⋊Dic17 |
| derived, Hall | C17×C127 ⋊ C4 |
| Sylow | C127 ⋊ Dic17 |
| Sylow | C17 ⋊ Dic127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2159 |
| commutator, hypocenter | C17×C127 | C4 |
| Fitting, socle | C2×C17×C127 | C2 |
| LCS | G ▷ C17×C127 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,17,127,2|a^2=d,b^a=b^16,c^a=c^1262162 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2159, Dic6477, (C127⋊C3)⋊Dic17, … |
| maximal normal subgroup of | C3×Dic2159, (C127⋊C3)⋊Dic17, Dic4318 |
| maximal quotient of | C3×Dic2159, Dic6477, Dic15113 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8636, 4);