Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | AGL(1,𝔽5)×C22⋊AGL(1,𝔽5) |
| Fitting | C22×C52 ⋊ C42 |
| Sylow | C52 ⋊ C4×C22⋊C4 |
533 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 533 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | D4×AGL(1,𝔽5)2, #72221700, #72221704, … |
| maximal normal subgroup of | D4×AGL(1,𝔽5)2, #72221700, #72221704, … |
| maximal quotient of | #72221610, #72221617, #72259240, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9819);