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 ⋊ #2290 |
696 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=g,d^2=e,b^a=be,c^a=cf,h^b=h^4,h^c=h^4136 conjugacy classes — view the full character table.
| maximal subgroup of | #12097618, #12097625, #12097655, … |
| maximal normal subgroup of | #12097618, #12097625, #12097655, … |
| maximal quotient of | #12020400, #12020429, #12020441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 7567);