Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#11717039 |
| Fitting | C22×C4×C52 ⋊ C22 |
| Sylow | C52 ⋊ C22×C22⋊C4 |
1584 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 1584 conjugacy classes of subgroups — too many to draw. Only its 264 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×#13104045, C2×#13106387, C2×#13104048, … |
| maximal normal subgroup of | C2×#13104045, C2×#13106387, C2×#13104048, … |
| maximal quotient of | C2×#13100574, #72221098, #72221102, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8497);