Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Fitting | C2×C53×#568 ⋊ C2 |
| Sylow | C53 ⋊ #63090 |
10836 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|f^2=h,g^2=h,b^a=bg,e^a=eh,g^a=gh,i^a=i^52,g^b=gh,i^b=i^52,d^c=dh1850 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1083424);