Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#386 ⋊ C4 |
| Sylow | C53 ⋊ #12574 |
994 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=e,b^2=f,b^a=bd,d^a=dg,g^a=gh,i^a=i^30,c^b=ch,e^b=eg,i^c=i^52,e^d=eh,i^e=i^52410 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1095820);