Finite Group DatabasebetaFinite Group Databasebeta| order | 14400 |
| isoclinism | isoclinic class of SL(2,𝔽5)2 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C1 |
| direct product | SL(2,𝔽5)2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, Fitting, socle, cosocle, hypercenter | C22 | A52 |
| commutator, hypocenter | G | C1 |
| LCS | G | |
| UCS | C1 ◁ C22 | |
248 conjugacy classes of subgroups; only the 10 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 10 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
81 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.