Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of #10597167 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×#10597167 |
| Fitting, socle | C3×C52 ⋊ C3⋊C8 |
| derived | C52⋊C3 ⋊ C3×C8 |
| Hall | C3×C52⋊C3 ⋊ C8 |
| Sylow | C52 ⋊ C3×C3⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10597167 |
| commutator, hypocenter | C52⋊C3 | C3×C8 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52 | C3⋊C8 |
| prime radical | C3×(C5⋊D5)⋊C3 | C4 |
| cosocle | #1043⋊C3 | C2×C3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C3 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 75 |
39 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AΓL(1,𝔽25), D3×#10597167, #72276825 |
| maximal normal subgroup of | C3×AΓL(1,𝔽25), D3×#10597167, #72276825 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 564);