Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C5×#4021 |
| Fitting | C2×C42×C52 ⋊ C2 |
| Sylow | C52 ⋊ C2×#124 |
768 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 254 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 | C2×#13105101, C2×C5×#66049, C2×#13105092 |
| maximal normal subgroup of | C2×#13105101, C2×C5×#66049, C2×#13105092 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8982);