Finite Group DatabasebetaFinite Group Databasebeta| order | 810 |
| isoclinism | isoclinic class of #4174 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#4178 |
| Fitting, Hall | C5×#732 ⋊ C2 |
| Sylow | #732 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C3×C5 | (C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C2×C3×C5 |
| Frattini | C32 | C3×C5×D3 |
| Fitting | C5×#732 | C2 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C3×C5 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4178, C5×#4178⋊C2, #4178⋊D5, … |
| maximal normal subgroup of | D5×#4178, C5×#4178⋊C2, #4178⋊D5, … |
| maximal quotient of | C5×#66325, C2×C5×#4178 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(810, 25);