Finite Group DatabasebetaFinite Group Databasebeta| order | 4544 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | C71⋊#564 |
| Sylow | C71 ⋊ #564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D71 |
| commutator, socle, prime radical, cosocle | C22×C71 | C24 |
| Fitting | #125×C71 | C2 |
| hypercenter | #125 | D71 |
| hypocenter | C71 | #564 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ #125 | |
172 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^6,71|a^2=e,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,g^d=g^70509 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4544, 1304);