Finite Group DatabasebetaFinite Group Databasebeta| order | 8522 |
| automorphism | Aut(G) order 18151860 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4261 |
| unambiguous semidirect product | C4261⋊C2 |
| Fitting, socle, derived, Sylow | C4261 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C4261 | C2 |
| LCS | G ▷ C4261 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,4261|b^a=b^42602132 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30684666, C2×D4261, D4261⋊C3, … |
| maximal normal subgroup of | #30684666, C2×D4261, D4261⋊C3, … |
| maximal quotient of | Dic4261, C2×D4261, C3×D4261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8522, 1);