Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C5×#103 ⋊ C2 |
| Sylow | C5 ⋊ #2036 |
316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 87 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=g,c^2=dg,e^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cf,h^b=h^4,e^c=eg,h^c=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2036, C2×#10601037, #12126780, … |
| maximal normal subgroup of | D5×#2036, C2×#10601037, #12126780, … |
| maximal quotient of | #12002602, #12002609, #12002692, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3119);