Finite Group DatabasebetaFinite Group Databasebeta| order | 6150 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C41 · Schur multiplier (H2) = C5 |
| direct product | C3×C41×C5⋊D5 |
| unambiguous semidirect product | C5⋊(C3×D5×C41) |
| Fitting, socle, Hall | C3×C52×C41 ⋊ C2 |
| derived, Sylow | C52 ⋊ C2×C3×C41 |
| Hall | C52×C41 ⋊ C2×C3 |
| Hall | C3×C52 ⋊ C2×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C41 | C5⋊D5 |
| commutator, hypocenter | C52 | C2×C3×C41 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C41 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C41 | |
64 conjugacy classes of subgroups.
1722 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C41×#1043, C3×#16861520, C3×C41×#1044, … |
| maximal normal subgroup of | C3×C41×#1043, C3×#16861520, C3×C41×#1044, … |
| maximal quotient of | C3×C41×#1039, C2×C3×C41×C5⋊D5, C9×C41×C5⋊D5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6150, 31);