Finite Group DatabasebetaFinite Group Databasebeta| order | 8050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D805 |
| unambiguous semidirect product | C7⋊(C5⋊D115) |
| unambiguous semidirect product | C23⋊(C5⋊D35) |
| Fitting, socle, derived, Hall | C52×C7×C23 ⋊ C2 |
| Hall | C52×C23 ⋊ D7 |
| Hall | C52×C7 ⋊ D23 |
| Hall | C7×C23 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D161 |
| Sylow | C23 ⋊ C5⋊D35 |
| Sylow | C7 ⋊ C5⋊D115 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C7×C23 | C2 |
| LCS | G ▷ C52×C7×C23 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^2,7,23|b^a=b^4,c^a=c^4,d^a=d^6,e^a=e^222014 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×C5⋊D35, D7×C5⋊D115, C5⋊D5×D161, … |
| maximal normal subgroup of | D23×C5⋊D35, D7×C5⋊D115, C5⋊D5×D161, … |
| maximal quotient of | C7⋊(C23⋊#1039), C2×C5⋊D805, C3×C5⋊D805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8050, 20);