Finite Group DatabasebetaFinite Group Databasebeta| order | 10950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C52×C73 ⋊ C2×C3 |
| derived | C5×C73 ⋊ C2×C3×C5 |
| Hall | C52×C73⋊C3 ⋊ C2 |
| Hall | C5×D365 ⋊ C3 |
| Hall | C73⋊C3 ⋊ C5×D5 |
| Sylow | C73 ⋊ C3×C5×D5 |
| Sylow | C52 ⋊ D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C5⋊(D73⋊C3) |
| commutator, cosocle, hypocenter | C5×C73 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C73 | C2×C3 |
| LCS | G ▷ C5×C73 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
360 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10950, 15);