Finite Group DatabasebetaFinite Group Databasebeta| order | 6150 |
| isoclinism | isoclinic class of C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C41 · Schur multiplier (H2) = C5 |
| direct product | C2×C41×C52⋊C3 |
| unambiguous semidirect product | (C2×C52)⋊(C3×C41) |
| unambiguous semidirect product | (C2×C52×C41)⋊C3 |
| Fitting, socle, Hall | C2×C52×C41 ⋊ C3 |
| derived, Sylow | C52 ⋊ C2×C3×C41 |
| Hall | C52×C41 ⋊ C2×C3 |
| Hall | C2×C52 ⋊ C3×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C41 | C52⋊C3 |
| commutator, hypocenter | C52 | C2×C3×C41 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C41 | C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C41 | |
24 conjugacy classes of subgroups.
902 conjugacy classes — view the full character table.
| maximal subgroup of | C41×#64470, #27134196, C41×#1039⋊C3, … |
| maximal normal subgroup of | C41×#64470, #27134196, C41×#1039⋊C3, … |
| maximal quotient of | C4×C41×C52⋊C3, C22×C41×C52⋊C3, C2×C41×C52⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6150, 27);