Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C25 ⋊ Q8 |
| Sylow | C25 ⋊ Dic6 |
| Sylow | C3 ⋊ Dic50 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×D25 |
| commutator, Fitting, cosocle | C2×C3×C25 | C22 |
| Frattini | C2×C5 | D3×D5 |
| socle, prime radical | C2×C3×C5 | C2×D5 |
| hypocenter | C3×C25 | Q8 |
| LCS | G ▷ C2×C3×C25 ▷ C3×C25 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 600 |
Polycyclic presentation:
2^3,3,5^2|a^2=c,b^2=c,e^5=f,b^a=bc,e^a=e^4f^4,f^a=f^4,d^b=d^281 conjugacy classes — view the full character table.
| maximal subgroup of | Dic6×D25, D75⋊Q8, D3×Dic50, … |
| maximal normal subgroup of | Dic6×D25, D75⋊Q8, D3×Dic50, … |
| maximal quotient of | #11924816, #11924817, Dic3⋊Dic25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 7);