Finite Group DatabasebetaFinite Group Databasebeta| order | 10050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C52⋊C3×D67 |
| Fitting, socle, derived, Hall | C52×C67 ⋊ C2×C3 |
| Hall | C67×C52⋊C3 ⋊ C2 |
| Hall | C52×D67 ⋊ C3 |
| Sylow | C67 ⋊ C2×C52⋊C3 |
| Sylow | C52 ⋊ C3×D67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C67 | C2×C3 |
| LCS | G ▷ C52×C67 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
385 conjugacy classes — view the full character table.
| maximal subgroup of | D67×#3874, D67×(C5⋊D5)⋊C3, C2×C52⋊C3×D67, … |
| maximal normal subgroup of | D67×#3874, D67×(C5⋊D5)⋊C3, C2×C52⋊C3×D67, … |
| maximal quotient of | C52⋊C3×Dic67, C2×C52⋊C3×D67, D67×C52⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10050, 26);