Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| isoclinism | isoclinic class of C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C31 · Schur multiplier (H2) = C5 |
| direct product | C2×C31×C52⋊C9 |
| unambiguous semidirect product | (C2×C52)⋊(C9×C31) |
| derived, Sylow | C52 ⋊ C2×C9×C31 |
| Hall | C2×C52×C31 ⋊ C9 |
| Hall | C52×C31 ⋊ C2×C9 |
| Hall | C2×C52 ⋊ C9×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C31 | C52⋊C3 |
| commutator, hypocenter | C52 | C2×C9×C31 |
| Frattini | C3 | C2×C31×C52⋊C3 |
| Fitting, socle, prime radical | C2×C3×C52×C31 | C3 |
| cosocle | C3×C52 | C2×C3×C31 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C3×C31 | |
40 conjugacy classes of subgroups.
2046 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31×#11744607, C31⋊#11744607, C31×#1039⋊C9, … |
| maximal normal subgroup of | C31×#11744607, C31⋊#11744607, C31×#1039⋊C9, … |
| maximal quotient of | C4×C31×C52⋊C9, C22×C31×C52⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 76);