Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| isoclinism | isoclinic class of #6728 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×GL(2,𝔽5) |
| derived | SL(2,𝔽5) ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C4×C5 | S5 |
| commutator, hypocenter | SL(2,𝔽5) | C4×C5 |
| Frattini | C4 | C5×S5 |
| socle | C2×C5 | A5⋊C4 |
| prime radical | C5×#6732 | C2 |
| cosocle | #6732 | C2×C5 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C4×C5 | |
99 conjugacy classes of subgroups.
120 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×GL(2,𝔽5), C2×C5×GL(2,𝔽5), D5×GL(2,𝔽5) |
| maximal normal subgroup of | C3×C5×GL(2,𝔽5), C2×C5×GL(2,𝔽5), D5×GL(2,𝔽5) |
| maximal quotient of | C3×C5×GL(2,𝔽5), C2×C5×GL(2,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.