Finite Group DatabasebetaFinite Group Databasebeta| order | 4498 |
| automorphism | Aut(G) order 4641936 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2249 |
| unambiguous semidirect product | C13⋊D173 |
| unambiguous semidirect product | C173⋊D13 |
| Fitting, socle, derived, Hall | C13×C173 ⋊ C2 |
| Sylow | C173 ⋊ D13 |
| Sylow | C13 ⋊ D173 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C173 | C2 |
| LCS | G ▷ C13×C173 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 186 |
| transitive degree | μt(G) = 2249 |
Polycyclic presentation:
2,13,173|b^a=b^12,c^a=c^1721126 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D2249, D6747, (C13⋊C3)⋊D173, … |
| maximal normal subgroup of | C3×D2249, (C13⋊C3)⋊D173, C5×D2249, … |
| maximal quotient of | C3×D2249, D6747, C5×D2249, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4498, 3);