Finite Group DatabasebetaFinite Group Databasebeta| order | 8450 |
| automorphism | Aut(G) order 13182000 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4225 |
| unambiguous semidirect product | C25⋊D169 |
| unambiguous semidirect product | C169⋊D25 |
| Fitting, derived, Hall | C25×C169 ⋊ C2 |
| Sylow | C169 ⋊ D25 |
| Sylow | C25 ⋊ D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C169 | C2 |
| Frattini, socle | C5×C13 | D65 |
| LCS | G ▷ C25×C169 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,13,5,13|b^5=d^4,c^13=e^12,b^a=b^4d,c^a=c^12e,d^a=d^4,e^a=e^122114 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30683334, #30683335, D25×D169, … |
| maximal normal subgroup of | #30683334, #30683335, D25×D169, … |
| maximal quotient of | Dic4225, C2×D4225, C3×D4225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8450, 4);