Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #23374 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×#6157 |
| commutator, socle, prime radical | C23×C53 | C23×C4 |
| Fitting | C53×#398 | C4 |
| cosocle | C22×Dic53 | C24 |
| hypercenter | #398 | #6157 |
| hypocenter | C53 | #23374 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #398 | |
548 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13568 |
Polycyclic presentation:
2^8,53|a^2=g,b^2=f,c^2=f,d^2=e,g^2=h,b^a=be,c^a=cf,d^a=defh,i^a=i^30,c^b=cefh,d^b=de,i^b=i^52,d^c=dh,i^c=i^52,i^d=i^52,i^g=i^52338 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1113308);