Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C27 |
| direct product | C2×C5×#4028 |
| Fitting | C2×C52×C22⋊C4 ⋊ C2 |
| Sylow | C52 ⋊ C2×#120 |
1456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#13105372 |
| maximal normal subgroup of | C2×#13105372 |
| maximal quotient of | C5×#10610717 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8994);