Finite Group DatabasebetaFinite Group Databasebeta| order | 10900 |
| isoclinism | isoclinic class of D109 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×C25×D109 |
| unambiguous semidirect product | C109⋊(C22×C25) |
| unambiguous semidirect product | (C2×C109)⋊(C2×C25) |
| Fitting | C2×C25×C109 ⋊ C2 |
| derived, Sylow | C109 ⋊ C22×C25 |
| Hall | C25×C109 ⋊ C22 |
30 conjugacy classes of subgroups.
2800 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C25×D109⋊C3, D3×C25×D109, C2×C3×C25×D109, … |
| maximal normal subgroup of | C2×C25×D109⋊C3, C2×C3×C25×D109 |
| maximal quotient of | D3×C25×D109, C2×C3×C25×D109, C2×C25×D327 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10900, 15);