Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| isoclinism | isoclinic class of C31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C9 · Schur multiplier (H2) = C5 |
| direct product | C2×C52×C31⋊C9 |
| derived, Sylow | C31 ⋊ C2×C52×C9 |
| Hall | C2×C52×C31 ⋊ C9 |
| Hall | C52×C31 ⋊ C2×C9 |
| Hall | C2×C31 ⋊ C52×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C52 | C31⋊C3 |
| commutator, hypocenter | C31 | C2×C52×C9 |
| Frattini | C3 | C2×C52×C31⋊C3 |
| Fitting, socle, prime radical | C2×C3×C52×C31 | C3 |
| cosocle | C3×C31 | C2×C3×C52 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C3×C52 | |
96 conjugacy classes of subgroups.
1950 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×Dic31⋊C9, C5×(C31⋊C9)⋊Dic5, C5×Dic5×C31⋊C9, … |
| maximal normal subgroup of | C52×Dic31⋊C9, C5×(C31⋊C9)⋊Dic5, C5×Dic5×C31⋊C9, … |
| maximal quotient of | C4×C52×C31⋊C9, C22×C52×C31⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 75);