Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1745 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D5 |
| commutator | C22×C5 | C2×C42 |
| Fitting | C43×C5 | C2 |
| socle, prime radical | C23×C5 | C22×C4 |
| cosocle | C22×C4×C5 | C23 |
| hypercenter | C43 | D5 |
| hypocenter | C5 | #1745 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C4 ◁ C43 | |
272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,c^a=cg,h^a=h^4184 conjugacy classes — view the full character table.
| maximal subgroup of | #11985845, #11985846, #11985898, … |
| maximal normal subgroup of | #11985845, #11985846, #11985898, … |
| maximal quotient of | #11989726, #11989733, #11989737, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2264);