Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| isoclinism | isoclinic class of C3⋊((C5⋊D5)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C5 |
| direct product | C31×C3⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | C3⋊(C31×(C5⋊D5)⋊C3) |
| unambiguous semidirect product | (C3⋊(C5⋊D5))⋊(C3×C31) |
| Fitting, socle | C3×C52×C31 ⋊ C2×C3 |
| derived | C3×C52 ⋊ C2×C3×C31 |
| Hall | C3×C31×C52⋊C3 ⋊ C2 |
| Hall | C52×C31 ⋊ C3×D3 |
| Hall | C3×C52⋊C3 ⋊ C2×C31 |
| Sylow | C52 ⋊ C3×D3×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C3⋊((C5⋊D5)⋊C3) |
| commutator, cosocle, hypocenter | C3×C52 | C2×C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C31 | C2×C3 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C31 | |
52 conjugacy classes of subgroups.
651 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 136);