Finite Group DatabasebetaFinite Group Databasebeta| order | 20160 |
| isoclinism | isoclinic class of A5×SL(2,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C2 |
| direct product | A5×SL(2,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, Fitting, cosocle, hypercenter | C2 | A5×GL(3,𝔽2) |
| commutator, hypocenter | G | C1 |
| socle | C2×A5 | GL(3,𝔽2) |
| LCS | G | |
| UCS | C1 ◁ C2 | |
250 conjugacy classes of subgroups; only the 6 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 6 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
55 conjugacy classes — view the full character table.
| maximal quotient of | SL(2,𝔽5)×SL(2,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.