Finite Group DatabasebetaFinite Group Databasebeta| order | 7950 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×C25×D53 |
| unambiguous semidirect product | C53⋊(C2×C3×C25) |
| Fitting, Hall | C3×C25×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C2×C3×C25 |
| Hall | C25×C53 ⋊ C2×C3 |
| Hall | C3×C53 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C25 | D53 |
| commutator, hypocenter | C53 | C2×C3×C25 |
| Frattini | C5 | C3×C5×D53 |
| Fitting | C3×C25×C53 | C2 |
| socle | C3×C5×C53 | C2×C5 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C3×C25 | |
24 conjugacy classes of subgroups.
2100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C25×#6157, C3×#19127058, C3×D25×D53, … |
| maximal normal subgroup of | C3×C25×#6157, C3×#19127058, C3×D25×D53, … |
| maximal quotient of | C3×C25×Dic53, C2×C3×C25×D53, C9×C25×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7950, 2);