Finite Group DatabasebetaFinite Group Databasebeta| order | 4556 |
| automorphism | Aut(G) order 2405568 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1139 |
| unambiguous semidirect product | C67⋊Dic17 |
| derived, Hall | C17×C67 ⋊ C4 |
| Sylow | C67 ⋊ Dic17 |
| Sylow | C17 ⋊ Dic67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1139 |
| commutator, hypocenter | C17×C67 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C17×C67 | C2 |
| LCS | G ▷ C17×C67 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 88 |
| transitive degree | μt(G) = 4556 |
Polycyclic presentation:
2,17,67,2|a^2=d,b^a=b^16,c^a=c^661142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic1139, Dic3417, (C67⋊C3)⋊Dic17, … |
| maximal normal subgroup of | C3×Dic1139, (C67⋊C3)⋊Dic17, C5×Dic1139, … |
| maximal quotient of | C3×Dic1139, Dic3417, C5×Dic1139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4556, 4);