Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #2392 |
696 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^4,h^c=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #11994398, #11994403, #12071571, … |
| maximal normal subgroup of | #11994398, #11994403, #12071571, … |
| maximal quotient of | #12020980, #12020999, #12021039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 7589);