Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C2×H(5,𝔽2)×C53 ⋊ C4 |
| Sylow | C53 ⋊ #60070 |
4892 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=g,e^2=h,b^a=bf,f^a=fh,i^a=i^30,g^b=gh,d^c=dh,i^e=i^52,i^g=i^52524 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1114723);