Finite Group DatabasebetaFinite Group Databasebeta| order | 810 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C34 · Schur multiplier (H2) = C36 |
| direct product | C34×D5 |
| unambiguous semidirect product | C5⋊(C2×C34) |
| Fitting, socle, Hall | C34×C5 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C34 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C34 | D5 |
| commutator, cosocle, hypocenter | C5 | C2×C34 |
| Frattini | C1 | G |
| Fitting, socle | C34×C5 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C34 | |
848 conjugacy classes of subgroups.
| transitive degree | μt(G) = 405 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C34×AGL(1,𝔽5), C33×ΓL(1,𝔽16), C32×C3⋊ΓL(1,𝔽16), … |
| maximal normal subgroup of | C34×AGL(1,𝔽5), C33×ΓL(1,𝔽16), C32×C3⋊ΓL(1,𝔽16), … |
| maximal quotient of | C34×Dic5, C2×C34×D5, D5×3−1+4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(810, 104);