Finite Group DatabasebetaFinite Group Databasebeta| order | 8050 |
| automorphism | Aut(G) order 10626000 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4025 |
| unambiguous semidirect product | C7⋊D575 |
| unambiguous semidirect product | C23⋊D175 |
| unambiguous semidirect product | C25⋊D161 |
| Fitting, derived, Hall | C7×C23×C25 ⋊ C2 |
| Hall | C23×C25 ⋊ D7 |
| Hall | C7×C25 ⋊ D23 |
| Hall | C7×C23 ⋊ D25 |
| Sylow | C25 ⋊ D161 |
| Sylow | C23 ⋊ D175 |
| Sylow | C7 ⋊ D575 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C7×C23×C25 | C2 |
| Frattini | C5 | D805 |
| socle | C5×C7×C23 | D5 |
| LCS | G ▷ C7×C23×C25 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,7,23,5|b^5=e^4,b^a=b^4e,c^a=c^6,d^a=d^22,e^a=e^42014 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D175, D7×D575, D25×D161, … |
| maximal normal subgroup of | D23×D175, D7×D575, D25×D161, … |
| maximal quotient of | Dic4025, C2×D4025, C3×D4025, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8050, 8);