Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C5 |
| direct product | C2×C4⋊C4×C5⋊D5 |
| Fitting | C2×C52×C4⋊C4 ⋊ C2 |
| Sylow | C52 ⋊ C22×C4⋊C4 |
1672 conjugacy classes of subgroups; only the 435 normal subgroups are shown.
This group has 1672 conjugacy classes of subgroups — too many to draw. Only its 435 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#106×C5⋊D5, C2×C4⋊C4×#1043, C2×#13100253, … |
| maximal normal subgroup of | C2×#106×C5⋊D5, C2×C4⋊C4×#1043, C2×#13100253, … |
| maximal quotient of | C2×#106×C5⋊D5, C2×#108×C5⋊D5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9382);