Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C4×D4×C53 ⋊ C4 |
| Sylow | C53 ⋊ #10788 |
1802 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=f,b^2=g,d^2=h,e^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,i^a=i^30,d^b=dh,e^b=eh,d^c=dh,e^c=eh,i^f=i^52596 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1092145);