Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#11717018 |
| Sylow | C52 ⋊ C22×C4⋊C4 |
1072 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 272 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×#87877, C2×#13106391, C2×#13103978, … |
| maximal normal subgroup of | C2×C4×#87877, C2×#13106391, C2×#13103978, … |
| maximal quotient of | #72221108 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8343);