Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C52×D12 |
| unambiguous semidirect product | C4⋊(C52×D3) |
| Fitting | C3×C4×C52 ⋊ C2 |
| Hall | C3×C52 ⋊ D4 |
| Sylow | C3 ⋊ C52×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C52 | C2×D3 |
| commutator, cosocle | C2×C3 | C22×C52 |
| Frattini | C2 | C2×C52×D3 |
| Fitting | C3×C4×C52 | C2 |
| socle | C2×C3×C52 | C22 |
| hypercenter | C4×C52 | D3 |
| hypocenter | C3 | C52×D4 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C52 ◁ C4×C52 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#6652, C5×#6654, C5×#6656, … |
| maximal normal subgroup of | C5×#6652, C5×#6654, C5×#6656, … |
| maximal quotient of | C52×#204, C52×D24, C52×Dic12, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 128);