Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C5 |
| direct product | C22⋊Q8×C5⋊D5 |
| Fitting | C52×C22⋊Q8 ⋊ C2 |
| Sylow | C52 ⋊ C2×C22⋊Q8 |
1288 conjugacy classes of subgroups; only the 265 normal subgroups are shown.
This group has 1288 conjugacy classes of subgroups — too many to draw. Only its 265 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×#525, C22⋊Q8×#1043, C5⋊D5×#546, … |
| maximal normal subgroup of | C5⋊D5×#525, C22⋊Q8×#1043, C5⋊D5×#546, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9510);