Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C53 ⋊ #62624 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×#6157 |
| commutator, socle | C2×C53 | C24×C8 |
| Fitting | C53×#568 | C4 |
| prime radical | #16811459 | C4 |
| cosocle | #88322 | C25 |
| hypercenter | #568 | #6157 |
| hypocenter | C53 | #62624 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C4 ◁ #568 | |
2038 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=f,f^2=g,g^2=h,i^a=i^30,e^b=eh,i^b=i^52,d^c=dh,i^f=i^52578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1116272);