Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D3×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C3×C25 ⋊ C2×C4 |
| Sylow | C25 ⋊ C4×D3 |
| Sylow | C3 ⋊ C4×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×D25 |
| commutator, hypocenter | C3×C25 | C2×C4 |
| Frattini | C2×C5 | D3×D5 |
| Fitting, cosocle | C2×C3×C25 | C22 |
| socle | C2×C3×C5 | C2×D5 |
| prime radical | C2×D75 | C2 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
Polycyclic presentation:
2^3,3,5^2|a^2=c,b^2=c,e^5=f,e^a=e^4f^4,f^a=f^4,d^b=d^284 conjugacy classes — view the full character table.
| maximal subgroup of | #11924879, #11924880, #11924912, … |
| maximal normal subgroup of | #11924879, #11924880, #11924912, … |
| maximal quotient of | #11924798, #11924800, Dic3×Dic25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 9);