Finite Group DatabasebetaFinite Group Databasebeta| order | 6150 |
| isoclinism | isoclinic class of D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C3×C52×D41 |
| Fitting, socle, Hall | C3×C52×C41 ⋊ C2 |
| derived, Sylow | C41 ⋊ C2×C3×C52 |
| Hall | C52×C41 ⋊ C2×C3 |
| Hall | C3×C41 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52 | D41 |
| commutator, hypocenter | C41 | C2×C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C41 | C2 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C3×C52 | |
64 conjugacy classes of subgroups.
1650 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C52×#4223, C3×C5×#11717964, C3×C5×D5×D41, … |
| maximal normal subgroup of | C3×C52×#4223, C3×C5×#11717964, C3×C5×D5×D41, … |
| maximal quotient of | C3×C52×Dic41, C2×C3×C52×D41, C52×C9×D41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6150, 28);