Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of D5×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C5×D5×C3⋊D3 |
| Fitting, socle | C2×C32×C52 ⋊ C22 |
| derived | C32×C5 ⋊ C23×C5 |
| Hall | C32×C52 ⋊ C23 |
| Sylow | C52 ⋊ C22×C3⋊D3 |
| Sylow | C32 ⋊ C22×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D5×C3⋊D3 |
| commutator, cosocle, hypocenter | C32×C5 | C23×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C52 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C2×C5 | |
444 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 727);