Finite Group DatabasebetaFinite Group Databasebeta| order | 4418 |
| automorphism | Aut(G) order 4775858 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2209 |
| unambiguous semidirect product | C2209⋊C2 |
| Fitting, derived, Sylow | C2209 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C2209 | C2 |
| Frattini, socle | C47 | D47 |
| LCS | G ▷ C2209 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 2209 |
| transitive degree | μt(G) = 2209 |
Polycyclic presentation:
2,47^2|b^47=c,b^a=b^46c^46,c^a=c^461106 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D2209, D6627, C5×D2209, … |
| maximal normal subgroup of | C3×D2209, C5×D2209, C7×D2209 |
| maximal quotient of | C3×D2209, D6627, C5×D2209, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4418, 1);