Finite Group DatabasebetaFinite Group Databasebeta| order | 8650 |
| isoclinism | isoclinic class of D173 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D173 |
| unambiguous semidirect product | C173⋊(C2×C52) |
| Fitting, socle, Hall | C52×C173 ⋊ C2 |
| derived, Sylow | C173 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D173 |
| commutator, hypocenter | C173 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C173 | C2 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C52 | |
32 conjugacy classes of subgroups.
2200 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×#10621924, C5×#16812340, C5×D5×D173, … |
| maximal normal subgroup of | C52×#10621924, C5×#16812340, C5×D5×D173, … |
| maximal quotient of | C52×Dic173, C2×C52×D173, C3×C52×D173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8650, 6);