Finite Group DatabasebetaFinite Group Databasebeta| order | 1500 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C5 |
| direct product | C3×C5×#1039 |
| derived | C52 ⋊ C3×C4×C5 |
| Hall | C3×C53 ⋊ C4 |
| Sylow | C53 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | C5⋊D5 |
| commutator, hypocenter | C52 | C3×C4×C5 |
| Frattini | C2 | C3×C5×C5⋊D5 |
| Fitting, socle, prime radical | C2×C3×C53 | C2 |
| cosocle | C2×C52 | C2×C3×C5 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C3×C5 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1500, 105);