Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C256 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C53 ⋊ C256 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C64 | #6157 |
| commutator, hypocenter | C53 | C256 |
| Fitting | C53×C64 | C4 |
| socle, prime radical | C2×C53 | C128 |
| cosocle | #20272534 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C64 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13568 |
Polycyclic presentation:
2^8,53|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,g^2=h,i^a=i^30,i^b=i^521088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1083473);