Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of #6057 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C5 |
| direct product | C3×#6057 |
| Fitting, socle, Hall | C3×C52 ⋊ Q8 |
| Sylow | C52 ⋊ C3×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #6057 |
| commutator, cosocle | C5⋊D5 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52 | Q8 |
| prime radical | C3×C5⋊D5 | C22 |
| hypocenter | C52 | C3×Q8 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C3 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30 |
24 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6057, C3×(D5⋊AGL(1,𝔽5))⋊C2, #6057⋊D3, … |
| maximal normal subgroup of | D3×#6057, C3×(D5⋊AGL(1,𝔽5))⋊C2, #6057⋊D3, … |
| maximal quotient of | C3×#87840, C2×C3×#6057, C9×#6057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 172);