Finite Group DatabasebetaFinite Group Databasebeta| order | 8468 |
| automorphism | Aut(G) order 8535744 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2117 |
| derived, Hall | C29×C73 ⋊ C4 |
| Sylow | C73 ⋊ Dic29 |
| Sylow | C29 ⋊ Dic73 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2117 |
| commutator, hypocenter | C29×C73 | C4 |
| Fitting, socle | C2×C29×C73 | C2 |
| LCS | G ▷ C29×C73 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,29,73,2|a^2=d,b^a=b^28,c^a=c^722120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2117, Dic6351, Dic2117⋊C3, … |
| maximal normal subgroup of | C3×Dic2117, Dic2117⋊C3, Dic4234 |
| maximal quotient of | C3×Dic2117, Dic6351, Dic14819 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8468, 4);