Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| isoclinism | isoclinic class of A52 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C22 |
| omega | Ω+(4,𝔽4) |
| direct product | A52 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | G | C1 |
| LCS | G | |
| UCS | C1 | |
113 conjugacy classes of subgroups.
25 conjugacy classes — view the full character table.
| derived subgroup of | A5×S5, S52, C2×A52, … |
| socle of | A5×S5, S52 |
| maximal subgroup of | A5×A6, GO+(4,𝔽4), #72219548, … |
| maximal normal subgroup of | GO+(4,𝔽4), #72219548, A5×S5, … |
| maximal quotient of | A5×SL(2,𝔽5), Ω+(4,𝔽5), A5×#11757162, … |
Past the SmallGroups library coverage — no SmallGroups id.