Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25×C5 |
| direct product | C2×#11716899 |
| Fitting | C22×C4×C52 ⋊ C4 |
| Sylow | C52 ⋊ C2×#95 |
896 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13104045, C2×#13104048, C2×C4×C4⋊#1044, … |
| maximal normal subgroup of | C2×#13104045, C2×#13104048, C2×C4×C4⋊#1044, … |
| maximal quotient of | C2×#13100332, #72221087, #72221089, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7252);