Finite Group DatabasebetaFinite Group Databasebeta| order | 4658 |
| automorphism | Aut(G) order 5067904 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2329 |
| unambiguous semidirect product | C17⋊D137 |
| unambiguous semidirect product | C137⋊D17 |
| Fitting, socle, derived, Hall | C17×C137 ⋊ C2 |
| Sylow | C137 ⋊ D17 |
| Sylow | C17 ⋊ D137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C137 | C2 |
| LCS | G ▷ C17×C137 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 154 |
| transitive degree | μt(G) = 2329 |
Polycyclic presentation:
2,17,137|b^a=b^16,c^a=c^1361166 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D2329, D6987, C5×D2329, … |
| maximal normal subgroup of | C3×D2329, C5×D2329, C7×D2329 |
| maximal quotient of | C3×D2329, D6987, C5×D2329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4658, 5);