Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C27 |
| direct product | C2×C5×#4083 |
| Fitting | C22×C52×D4 ⋊ C2 |
| Sylow | C52 ⋊ C2×#120 |
1560 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#13106387, C2×C5×#66051, C2×#13106268, … |
| maximal normal subgroup of | C2×#13106387, C2×C5×#66051, C2×#13106268, … |
| maximal quotient of | C2×C5×#65366, C5×#10615053, C5×#10614667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9307);