Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of D52×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | D52×C3⋊D3 |
| Fitting, socle, derived, Hall | C32×C52 ⋊ C23 |
| Sylow | C52 ⋊ C22×C3⋊D3 |
| Sylow | C32 ⋊ C2×D52 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C52 | C23 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 | |
444 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 90 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #72222479, D32×D52, #72222582, … |
| maximal normal subgroup of | D32×D52, #72222582, C3⋊D3×D5⋊AGL(1,𝔽5), … |
| maximal quotient of | #72222479, C3⋊D3×#6036, #72229316, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 675);