Finite Group DatabasebetaFinite Group Databasebeta| order | 28736 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C449 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C449 | C64 |
| prime radical | D449 | C32 |
| cosocle | #28385441 | C2 |
| LCS | G ▷ C449 | |
| UCS | C1 | |
14 conjugacy classes of subgroups.
| transitive degree | μt(G) = 449 |
Polycyclic presentation:
2^6,449|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^391,g^b=g^221,g^c=g^349,g^d=g^122,g^e=g^67,g^f=g^44871 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28736, 1684);