Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of (C5⋊D5)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C5 |
| direct product | C4×(C5⋊D5)⋊C3 |
| unambiguous semidirect product | (C4×C5⋊D5)⋊C3 |
| Fitting | C4×C52 ⋊ C2×C3 |
| derived, Sylow | C52 ⋊ C2×C3×C4 |
| Hall | C4×C5⋊D5 ⋊ C3 |
| Hall | C52⋊C3 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | (C5⋊D5)⋊C3 |
| commutator, hypocenter | C52 | C2×C3×C4 |
| Frattini | C2 | C2×(C5⋊D5)⋊C3 |
| Fitting | C4×C52 | C2×C3 |
| socle, cosocle | C2×C52 | C22×C3 |
| prime radical | C2×(C5⋊D5)⋊C3 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C4 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
40 conjugacy classes — view the full character table.
| maximal subgroup of | #11925007, #11925008, C8×(C5⋊D5)⋊C3, … |
| maximal normal subgroup of | #11925007, #11925008, C8×(C5⋊D5)⋊C3, … |
| maximal quotient of | C8×(C5⋊D5)⋊C3, #87799⋊C3, C4×#1039⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 68);