Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C31⋊C3×#3874 |
| unambiguous semidirect product | (C31×#3874)⋊C3 |
| Fitting, socle, Hall | C52×C31 ⋊ C3×D3 |
| derived | C31×C52⋊C3 ⋊ C2×C3 |
| Hall | C52⋊C3×C31⋊C3 ⋊ C2 |
| Sylow | C31 ⋊ C3×#3874 |
| Sylow | C52 ⋊ D3×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C31×C52⋊C3 | C2×C3 |
| Fitting, socle | C52×C31 | C3×D3 |
| LCS | G ▷ C31×C52⋊C3 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
169 conjugacy classes — view the full character table.
| maximal subgroup of | #3874×D31⋊C3, #3874⋊(D31⋊C3), C31⋊C3×#3874⋊C2, … |
| maximal normal subgroup of | #3874×D31⋊C3, #3874⋊(D31⋊C3), C31⋊C3×#3874⋊C2, … |
| maximal quotient of | C31⋊C3×#64470, C2×C31⋊C3×#3874 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 98);