Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #1925 |
290 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=df,c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^4,e^c=eg118 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1925, C2×#10600255, #12101694, … |
| maximal normal subgroup of | D5×#1925, C2×#10600255, #12101694, … |
| maximal quotient of | #11997473, #11997501, #11997613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2337);