Finite Group DatabasebetaFinite Group Databasebeta| order | 9206 |
| automorphism | Aut(G) order 21183006 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4603 |
| unambiguous semidirect product | C4603⋊C2 |
| Fitting, socle, derived, Sylow | C4603 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C4603 | C2 |
| LCS | G ▷ C4603 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,4603|b^a=b^46022303 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4603, D4603⋊C3, C3×D4603, … |
| maximal normal subgroup of | C2×D4603, D4603⋊C3, C3×D4603 |
| maximal quotient of | Dic4603, C2×D4603, C3×D4603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9206, 1);