Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C5 |
| direct product | C3×#6034 |
| derived, Sylow | C52 ⋊ C3×C8 |
| Hall | C3×C52 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #1044 |
| commutator, hypocenter | C52 | C3×C8 |
| Frattini | C2 | C3×#1044 |
| Fitting, socle, prime radical | C2×C3×C52 | C4 |
| cosocle | #1039 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C3 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5⋊#170, C3×#87834, D3×#6034, … |
| maximal normal subgroup of | C3×D5⋊#170, C3×#87834, D3×#6034, … |
| maximal quotient of | C3×#87765, C2×C3×#6034, C9×#6034, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 75);