Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| isoclinism | isoclinic class of SL(2,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C5×#6732 |
| derived | SL(2,𝔽5) ⋊ C22×C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2×C3×C4×C5 | A5 |
| commutator, hypocenter | SL(2,𝔽5) | C22×C3×C5 |
| Frattini, cosocle | C2 | C22×C3×C5×A5 |
| socle | C22×C3×C5 | C2×A5 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C3×C4×C5 | |
468 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C5×GL(2,𝔽5), C2×C3×D5×#6732 |
| maximal normal subgroup of | C2×C3×C5×GL(2,𝔽5), C2×C3×D5×#6732 |
Past the SmallGroups library coverage — no SmallGroups id.