Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of C3⋊(C5⋊D5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C3⋊#1039 |
| unambiguous semidirect product | (C2×C3)⋊#1039 |
| derived, Hall | C3×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ C2×Dic3 |
| Sylow | C3 ⋊ C2×#1039 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊(C5⋊D5) |
| commutator, hypocenter | C3×C52 | C2×C4 |
| Frattini | C2 | C2×C3⋊(C5⋊D5) |
| Fitting, socle, prime radical | C22×C3×C52 | C2 |
| cosocle | C2×C3×C52 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C22 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#1039, #11925118, (C2×D3)⋊#1039, … |
| maximal normal subgroup of | Dic3×#1039, #11925118, (C2×D3)⋊#1039, … |
| maximal quotient of | C2×C3⋊#6029, #11925245, C4×C3⋊#1039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 139);