Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×#677 |
| Fitting | C23×C5×C8 ⋊ C2 |
| Sylow | C5 ⋊ C23×SD16 |
1720 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | #12006103, #12006107, #12006130, … |
| maximal normal subgroup of | #12006103, #12006107, #12006130, … |
| maximal quotient of | C23×#3953, C23×#3948, C23×#3949, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21132);