Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of D3×D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#67149 |
| derived | C32×C5 ⋊ C2×C4×C5 |
| Hall | C32×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ #624 |
| Sylow | C32 ⋊ C4×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D3×D15 |
| commutator, hypocenter | C32×C5 | C2×C4×C5 |
| Frattini | C2 | C5×D3×D15 |
| Fitting, socle | C2×C32×C52 | C22 |
| prime radical | C2×C5×C3⋊D15 | C2 |
| cosocle | C2×C32×C5 | C22×C5 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C2×C5 | |
176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72231330 |
| maximal normal subgroup of | #72231330 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 473);