Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of #6053 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×#6053 |
| Fitting, socle, Hall | C3×C52 ⋊ C8 |
| derived, Sylow | C52 ⋊ C3×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #6053 |
| commutator, hypocenter | C52 | C3×C8 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52 | C8 |
| prime radical | C3×C5⋊D5 | C4 |
| cosocle | #1043 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30 |
33 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6053, C3×#6053⋊C2, #11925748, … |
| maximal normal subgroup of | D3×#6053, C3×#6053⋊C2, #11925748, … |
| maximal quotient of | C3×#87822, C2×C3×#6053, C9×#6053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 155);