Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C53 ⋊ #60344 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×#6157 |
| commutator, socle | C22×C53 | C24×C4 |
| Fitting, prime radical | C53×#537 | C4 |
| cosocle | C2×Dic53 | C25 |
| hypercenter | #537 | #6157 |
| hypocenter | C53 | #60344 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ #537 | |
1664 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6784 |
Polycyclic presentation:
2^8,53|a^2=g,b^2=f,c^2=f,e^2=g,g^2=h,b^a=bf,c^a=ch,d^a=df,i^a=i^30,c^b=cf,d^b=dh,e^b=eh,i^b=i^52,i^c=i^52,i^e=i^30,i^g=i^52362 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1116236);