Finite Group DatabasebetaFinite Group Databasebeta| order | 10050 |
| isoclinism | isoclinic class of C67⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C2×C52×C67⋊C3 |
| unambiguous semidirect product | (C2×C67)⋊(C3×C52) |
| unambiguous semidirect product | (C2×C5×C67)⋊(C3×C5) |
| Fitting, socle, Hall | C2×C52×C67 ⋊ C3 |
| derived, Sylow | C67 ⋊ C2×C3×C52 |
| Hall | C52×C67 ⋊ C2×C3 |
| Hall | C2×C67 ⋊ C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | C67⋊C3 |
| commutator, cosocle, hypocenter | C67 | C2×C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C67 | C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C52 | |
64 conjugacy classes of subgroups.
1250 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10050, 29);