Finite Group DatabasebetaFinite Group Databasebeta| order | 1500 |
| isoclinism | isoclinic class of C3⋊#92534 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#92534 |
| Fitting, derived, Hall | C3×C5×C25 ⋊ C4 |
| Sylow | C5×C25 ⋊ Dic3 |
| Sylow | C3 ⋊ #92534 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C5×C25 | C4 |
| Frattini | C5 | C3⋊#1042 |
| socle | C3×C52 | AGL(1,𝔽5) |
| prime radical, cosocle | C3×C5×D25 | C2 |
| LCS | G ▷ C3×C5×C25 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 300 |
Polycyclic presentation:
2^2,3,5^3|a^2=b,d^5=f,c^a=c^2,d^a=d^2f,e^a=e^4,f^a=f^2,d^b=d^4f^4,f^b=f^4108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1500, 56);