Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C5 |
| direct product | C8×C52⋊C3 |
| unambiguous semidirect product | (C52×C8)⋊C3 |
| Fitting, Hall | C52×C8 ⋊ C3 |
| derived, Sylow | C52 ⋊ C3×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | C52⋊C3 |
| commutator, hypocenter | C52 | C3×C8 |
| Frattini | C4 | C2×C52⋊C3 |
| Fitting | C52×C8 | C3 |
| socle | C2×C52 | C3×C4 |
| prime radical | C2×C52⋊C3 | C4 |
| cosocle | C4×C52 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C8 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | #11924973, #87756⋊C3, C16×C52⋊C3, … |
| maximal normal subgroup of | #11924973, #87756⋊C3, C16×C52⋊C3, … |
| maximal quotient of | C16×C52⋊C3, C2×C8×C52⋊C3, C8×C52⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 47);