Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C5 |
| direct product | C3×C4×C5⋊D5 |
| Fitting | C3×C4×C52 ⋊ C2 |
| derived, Sylow | C52 ⋊ C2×C3×C4 |
| Hall | C3×C52 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | C5⋊D5 |
| commutator, hypocenter | C52 | C2×C3×C4 |
| Frattini | C2 | C2×C3×C5⋊D5 |
| Fitting | C3×C4×C52 | C2 |
| socle | C2×C3×C52 | C22 |
| prime radical | C2×C3×C5⋊D5 | C2 |
| cosocle | C2×C52 | C22×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C4 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#87767, C3×#87769, C3⋊C8×C5⋊D5, … |
| maximal normal subgroup of | C3×#87767, C3×#87769, C3⋊C8×C5⋊D5, … |
| maximal quotient of | C3×C8×C5⋊D5, C3×#87799, C3×C4×#1039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 122);