Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| isoclinism | isoclinic class of #6728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×GL(2,𝔽5) |
| derived | SL(2,𝔽5) ⋊ C2×C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2×C4×C5 | S5 |
| commutator, hypocenter | SL(2,𝔽5) | C2×C4×C5 |
| Frattini | C4 | C2×C5×S5 |
| socle | C22×C5 | A5⋊C4 |
| prime radical | C2×C5×#6732 | C2 |
| cosocle | #6732 | C22×C5 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C4×C5 | |
340 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
240 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×C5×GL(2,𝔽5) |
| maximal normal subgroup of | C2×C3×C5×GL(2,𝔽5) |
| maximal quotient of | C2×C3×C5×GL(2,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.