Finite Group DatabasebetaFinite Group Databasebeta| order | 10950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C3×C5⋊D365 |
| unambiguous semidirect product | C5⋊(C3×D365) |
| Fitting, socle, Hall | C3×C52×C73 ⋊ C2 |
| derived, Hall | C52×C73 ⋊ C2×C3 |
| Hall | C3×C73 ⋊ C5⋊D5 |
| Hall | C3×C52 ⋊ D73 |
| Sylow | C73 ⋊ C3×C5⋊D5 |
| Sylow | C52 ⋊ C3×D73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C5⋊D365 |
| commutator, cosocle, hypocenter | C52×C73 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C73 | C2 |
| LCS | G ▷ C52×C73 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
2742 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×D365, C3×C5⋊D5×D73, C3×#20300492, … |
| maximal normal subgroup of | C3×D5×D365, C3×C5⋊D5×D73, C3×#20300492, … |
| maximal quotient of | C3×#20300482, C2×C3×C5⋊D365, C9×C5⋊D365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10950, 36);