Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C128 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D53⋊C128 |
| derived, Sylow | C53 ⋊ C2×C128 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C64 | #6157 |
| commutator, hypocenter | C53 | C2×C128 |
| Frattini | C32 | C2×#6157 |
| Fitting | C53×C64 | C4 |
| socle | C2×C53 | C2×C64 |
| prime radical | C2×D53 | C64 |
| cosocle | #16810342 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C64 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6784 |
Polycyclic presentation:
2^8,53|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,g^2=h,i^a=i^30,i^b=i^52,i^c=i^521088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1084871);