Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| isoclinism | isoclinic class of #90646 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×#90646 |
| derived, Hall | C52⋊C9 ⋊ C2×C31 |
| Hall | C31×C52⋊C9 ⋊ C2 |
| Hall | C52×C31 ⋊ D9 |
| Sylow | C52 ⋊ D9×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | #90646 |
| commutator, cosocle, hypocenter | C52⋊C9 | C2×C31 |
| Frattini | C3 | C31×#3874 |
| Fitting, socle | C3×C52×C31 | D3 |
| LCS | G ▷ C52⋊C9 | |
| UCS | C1 ◁ C31 | |
40 conjugacy classes of subgroups.
744 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#90646⋊C2, #90646⋊D31, D31×#90646, … |
| maximal normal subgroup of | C31×#90646⋊C2, #90646⋊D31, D31×#90646, … |
| maximal quotient of | C31×#11744607, C2×C31×#90646 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 66);