Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D52×C22⋊C4 |
| Fitting | C52×C22⋊C4 ⋊ C22 |
| Sylow | C52 ⋊ C22×C22⋊C4 |
1480 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 1480 conjugacy classes of subgroups — too many to draw. Only its 256 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C4×D5⋊AGL(1,𝔽5), #72221713, #72221717, … |
| maximal normal subgroup of | C22⋊C4×D5⋊AGL(1,𝔽5), #72221713, #72221717, … |
| maximal quotient of | #72221783, D52×#104, #72221809, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7718);