Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #2324 |
668 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=eg,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^4,c^b=ce,h^c=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #12105021, #12105025, #12105051, … |
| maximal normal subgroup of | #12105021, #12105025, #12105051, … |
| maximal quotient of | #12020548, #12020593, #12020604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 7576);