Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C53×H(3,𝔽4) ⋊ C4 |
| Sylow | C53 ⋊ #34512 |
2576 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^8,53|a^2=h,b^2=f,c^2=h,e^2=h,b^a=bf,c^a=cg,d^a=dg,e^a=ef,i^a=i^23,c^b=cg,d^b=df,i^c=i^23,i^e=i^30,i^h=i^52323 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1114623);