Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| direct product | D5×SL(2,𝔽5) |
| unambiguous semidirect product | C5⋊(C2×SL(2,𝔽5)) |
| derived | C5×SL(2,𝔽5) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×A5 |
| commutator, hypocenter | C5×SL(2,𝔽5) | C2 |
| Fitting, socle, cosocle | C2×C5 | C2×A5 |
| LCS | G ▷ C5×SL(2,𝔽5) | |
| UCS | C1 ◁ C2 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
36 conjugacy classes — view the full character table.
| maximal subgroup of | A5×SL(2,𝔽5), C3×D5×SL(2,𝔽5), C2×D5×SL(2,𝔽5), … |
| maximal normal subgroup of | C3×D5×SL(2,𝔽5), C2×D5×SL(2,𝔽5), D5×#6732, … |
| maximal quotient of | Dic5×SL(2,𝔽5), C3×D5×SL(2,𝔽5), C2×D5×SL(2,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 480);