Finite Group DatabasebetaFinite Group Databasebeta| order | 8650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D865 |
| unambiguous semidirect product | C173⋊(C5⋊D5) |
| Fitting, socle, derived, Hall | C52×C173 ⋊ C2 |
| Sylow | C173 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D173 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C173 | C2 |
| LCS | G ▷ C52×C173 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^2,173|b^a=b^4,c^a=c^4,d^a=d^1722164 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31772425, #31772426, #31772429, … |
| maximal normal subgroup of | #31772425, #31772426, #31772429, … |
| maximal quotient of | #31772415, C2×C5⋊D865, C3×C5⋊D865, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8650, 10);