Finite Group DatabasebetaFinite Group Databasebeta| order | 810 |
| isoclinism | isoclinic class of #733⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#733⋊C2 |
| unambiguous semidirect product | #733⋊(C2×C5) |
| Fitting, Hall | C5×#733 ⋊ C2 |
| derived, Sylow | #733 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #733⋊C2 |
| commutator, cosocle, hypocenter | #733 | C2×C5 |
| Frattini | C32 | C5×C3⋊D3 |
| Fitting | C5×#733 | C2 |
| socle | C3×C5 | #272 |
| LCS | G ▷ #733 | |
| UCS | C1 ◁ C5 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
65 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#733⋊C2, C2×C5×#733⋊C2 |
| maximal normal subgroup of | D5×#733⋊C2, C2×C5×#733⋊C2 |
| maximal quotient of | C5×#733⋊C4, C2×C5×#733⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(810, 46);