Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C5 |
| direct product | C2×#11716665 |
| Fitting | C2×C52×C16 ⋊ C2 |
| Sylow | C52 ⋊ C2×M32 |
360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×M32×C5⋊D5, C2×#13100224, C2×#13100223, … |
| maximal normal subgroup of | C2×M32×C5⋊D5, C2×#13100224, C2×#13100223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5115);