Finite Group DatabasebetaFinite Group Databasebeta| order | 1500 |
| isoclinism | isoclinic class of C3⋊(C5⋊(C5⋊D5)) |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C53 |
| unambiguous semidirect product | C3⋊#92553 |
| derived, Hall | C3×C53 ⋊ C4 |
| Sylow | C53 ⋊ Dic3 |
| Sylow | C3 ⋊ #92553 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C5⋊(C5⋊D5)) |
| commutator, hypocenter | C3×C53 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C53 | C2 |
| LCS | G ▷ C3×C53 | |
| UCS | C1 ◁ C2 | |
384 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1500 |
Polycyclic presentation:
2^2,3,5^3|a^2=b,c^a=c^2,d^a=d^4,e^a=e^4,f^a=f^4378 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1500, 110);