Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C31 · Schur multiplier (H2) = C3×C5 |
| direct product | C32×C31×C5⋊D5 |
| unambiguous semidirect product | C5⋊(C32×D5×C31) |
| Fitting, socle, Hall | C32×C52×C31 ⋊ C2 |
| derived, Sylow | C52 ⋊ C2×C32×C31 |
| Hall | C52×C31 ⋊ C2×C32 |
| Hall | C32×C52 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C31 | C5⋊D5 |
| commutator, cosocle, hypocenter | C52 | C2×C32×C31 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C31 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C32×C31 | |
192 conjugacy classes of subgroups.
3906 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D52×C31, C32×(C5⋊D5)⋊D31, C32×C5⋊D5×D31, … |
| maximal normal subgroup of | C32×D52×C31, C32×(C5⋊D5)⋊D31, C32×C5⋊D5×D31, … |
| maximal quotient of | C32×C31×#1039, C2×C32×C31×C5⋊D5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 161);