Finite Group DatabasebetaFinite Group Databasebeta| order | 10050 |
| isoclinism | isoclinic class of #3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×#3874 |
| Fitting, socle, Hall | C52×C67 ⋊ D3 |
| derived, Hall | C52⋊C3 ⋊ C2×C67 |
| Hall | C67×C52⋊C3 ⋊ C2 |
| Sylow | C52 ⋊ D3×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | #3874 |
| commutator, cosocle, hypocenter | C52⋊C3 | C2×C67 |
| Frattini | C1 | G |
| Fitting, socle | C52×C67 | D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C67 | |
24 conjugacy classes of subgroups.
871 conjugacy classes — view the full character table.
| maximal subgroup of | C67×#3874⋊C2, #3874⋊D67, D67×#3874, … |
| maximal normal subgroup of | C67×#3874⋊C2, #3874⋊D67, D67×#3874, … |
| maximal quotient of | C67×#64470, C2×C67×#3874, C67×#90646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10050, 19);