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 ⋊ #34256 |
5898 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^8,53|a^2=h,c^2=gh,b^a=bf,c^a=cg,e^a=ef,i^a=i^23,d^b=df,i^c=i^30,i^h=i^52530 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1114367);