Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of #67150 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#67153 |
| Hall | C32×C52 ⋊ Q8 |
| Sylow | C52 ⋊ #627 |
| Sylow | C32 ⋊ C5×Dic10 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D3×D15 |
| commutator, cosocle | C2×C32×C5 | C22×C5 |
| Frattini | C2 | C5×D3×D15 |
| Fitting, socle, prime radical | C2×C32×C52 | C22 |
| hypocenter | C32×C5 | C5×Q8 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2×C5 | |
136 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
255 conjugacy classes — view the full character table.
| maximal subgroup of | #72231364 |
| maximal normal subgroup of | #72231364 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 477);