Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D5×C4⋊AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(D5×C4⋊C4) |
| Fitting | C2×C4×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ C22×C4⋊C4 |
863 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×D5×AGL(1,𝔽5), C2×AGL(1,𝔽5)×C4⋊AGL(1,𝔽5), C2×#13107456 |
| maximal normal subgroup of | C2×D4×D5×AGL(1,𝔽5), C2×AGL(1,𝔽5)×C4⋊AGL(1,𝔽5), C2×#13107456 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9965);