Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×D5×#102 |
| Fitting | C2×C5×#102 ⋊ C2 |
| Sylow | C5 ⋊ C22×#102 |
1072 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D5×#102, D5×#1762, #12097108, … |
| maximal normal subgroup of | C4×D5×#102, D5×#1762, #12097108, … |
| maximal quotient of | C2×D5×D4⋊C8, D5×#1486, C2×#10598965, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12551);