Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×Q8×C22⋊D5 |
| Fitting | C23×C5×Q8 ⋊ C2 |
| Sylow | C5 ⋊ C2×D4×Q8 |
1568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #11990982, #12114664, #101×C22⋊D5, … |
| maximal normal subgroup of | #11990982, #12114664, #101×C22⋊D5, … |
| maximal quotient of | C2×Q8×#685, C2×Q8×C22⋊Dic5, C2×C4⋊C4×C22⋊D5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21230);