Finite Group DatabasebetaFinite Group Databasebeta| order | 8258 |
| automorphism | Aut(G) order 17044512 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4129 |
| unambiguous semidirect product | C4129⋊C2 |
| Fitting, socle, derived, Sylow | C4129 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C4129 | C2 |
| LCS | G ▷ C4129 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,4129|b^a=b^41282066 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30658260, C2×D4129, D4129⋊C3, … |
| maximal normal subgroup of | #30658260, C2×D4129, D4129⋊C3, … |
| maximal quotient of | Dic4129, C2×D4129, C3×D4129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8258, 1);