Finite Group DatabasebetaFinite Group Databasebeta| order | 6150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C41⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | (C5⋊D205)⋊C3 |
| Fitting, socle, derived, Hall | C52×C41 ⋊ C2×C3 |
| Hall | C41×C52⋊C3 ⋊ C2 |
| Hall | C5⋊D205 ⋊ C3 |
| Hall | C52⋊C3 ⋊ D41 |
| Sylow | C41 ⋊ (C5⋊D5)⋊C3 |
| Sylow | C52 ⋊ C3×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C41 | C2×C3 |
| LCS | G ▷ C52×C41 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,41|c^a=c^4,d^a=d^4,e^a=e^40,c^b=cd,d^b=c^2d^3230 conjugacy classes — view the full character table.
| maximal subgroup of | #3874⋊D41, #16861519⋊C3, #16861518⋊C3, … |
| maximal normal subgroup of | #3874⋊D41, #16861519⋊C3, #16861518⋊C3, … |
| maximal quotient of | #16861497⋊C3, C2×C41⋊((C5⋊D5)⋊C3), C41⋊((C5⋊D5)⋊C9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6150, 24);