Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#6014 |
| derived, Hall | C3×C25 ⋊ C8 |
| Sylow | C25 ⋊ C3⋊C8 |
| Sylow | C3 ⋊ #6014 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D75 |
| commutator, hypocenter | C3×C25 | C8 |
| Frattini | C4×C5 | D15 |
| Fitting, cosocle | C3×C4×C25 | C2 |
| socle, prime radical | C2×C3×C5 | Dic5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C4 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 600 |
Polycyclic presentation:
2^3,3,5^2|a^2=b,b^2=c,e^5=f,d^a=d^2,e^a=e^4f^4,f^a=f^4156 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊C8×D25, #11924799, D3×#6014, … |
| maximal normal subgroup of | C3⋊C8×D25, #11924799, D3×#6014, … |
| maximal quotient of | C3⋊#87707, C2×C3⋊#6014, C9⋊#6014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 3);