Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×C64 ⋊ C4 |
| Sylow | C53 ⋊ #7510 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C2×#6157 |
| commutator, socle | C2×C53 | C4×C32 |
| Fitting | C53×C64 | C4 |
| prime radical | C2×D53 | C2×C32 |
| cosocle | C32×D53 | C22 |
| hypercenter | C64 | #6157 |
| hypocenter | C53 | #7510 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C32 ◁ C64 | |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,g^2=h,b^a=bh,i^b=i^30,i^d=i^52992 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1084787);