Finite Group DatabasebetaFinite Group Databasebeta| order | 6150 |
| isoclinism | isoclinic class of #3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×#3874 |
| Fitting, socle, Hall | C52×C41 ⋊ D3 |
| derived, Hall | C52⋊C3 ⋊ C2×C41 |
| Hall | C41×C52⋊C3 ⋊ C2 |
| Sylow | C52 ⋊ D3×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | #3874 |
| commutator, hypocenter | C52⋊C3 | C2×C41 |
| Frattini | C1 | G |
| Fitting, socle | C52×C41 | D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C41 | |
24 conjugacy classes of subgroups.
533 conjugacy classes — view the full character table.
| maximal subgroup of | C41×#3874⋊C2, #3874⋊D41, D41×#3874, … |
| maximal normal subgroup of | C41×#3874⋊C2, #3874⋊D41, D41×#3874, … |
| maximal quotient of | C41×#64470, C2×C41×#3874, C41×#90646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6150, 21);