Finite Group DatabasebetaFinite Group Databasebeta| order | 8042 |
| automorphism | Aut(G) order 16164420 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4021 |
| unambiguous semidirect product | C4021⋊C2 |
| Fitting, socle, derived, Sylow | C4021 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C4021 | C2 |
| LCS | G ▷ C4021 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,4021|b^a=b^40202012 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30632675, C2×D4021, D4021⋊C3, … |
| maximal normal subgroup of | #30632675, C2×D4021, D4021⋊C3, … |
| maximal quotient of | Dic4021, C2×D4021, C3×D4021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8042, 1);