Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽5)×A5 |
| Fitting | C5 ⋊ C4×A5 |
| socle, derived | C5×A5 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C5×A5 | C4 |
| Fitting | C5 | C4×A5 |
| prime radical | D5×A5 | C2 |
| cosocle | D5 | C2×A5 |
| LCS | G ▷ C5×A5 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 10 |
| transitive degree | μt(G) = 25 |
25 conjugacy classes — view the full character table.
| maximal subgroup of | A5×S5, AGL(1,𝔽5)×S5, C2×AGL(1,𝔽5)×A5 |
| maximal normal subgroup of | AGL(1,𝔽5)×S5, C2×AGL(1,𝔽5)×A5 |
| maximal quotient of | #72277233, C2×AGL(1,𝔽5)×A5, AGL(1,𝔽5)×SL(2,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 940);