Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C5×#64679 |
| Fitting | C4×C52×C8 ⋊ C2 |
| Sylow | C52 ⋊ D4⋊C8 |
208 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
460 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72223107 |
| maximal normal subgroup of | #72223107 |
| maximal quotient of | C5×#10597932, C5×#10597934 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1726);