Finite Group DatabasebetaFinite Group Databasebeta| order | 8222 |
| automorphism | Aut(G) order 16896210 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4111 |
| unambiguous semidirect product | C4111⋊C2 |
| Fitting, socle, derived, Sylow | C4111 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C4111 | C2 |
| LCS | G ▷ C4111 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,4111|b^a=b^41102057 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4111, D4111⋊C3, C3×D4111, … |
| maximal normal subgroup of | C2×D4111, D4111⋊C3, C3×D4111 |
| maximal quotient of | Dic4111, C2×D4111, C3×D4111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8222, 1);