Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C5×#4086 |
| Fitting | C22×C52×D4 ⋊ C2 |
| Sylow | C52 ⋊ C2×#127 |
1232 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 286 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#13106199, C2×C5×#66049, C2×C5×D5×#127, … |
| maximal normal subgroup of | C2×#13106199, C2×C5×#66049, C2×C5×D5×#127, … |
| maximal quotient of | C5×#10614894 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9300);