Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×C4⋊Q8×C53 ⋊ C4 |
| Sylow | C53 ⋊ #22406 |
1474 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=g,b^2=h,d^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^30,d^b=de,i^b=i^52,g^c=gh,i^c=i^52,i^d=i^52,i^g=i^52419 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1109693);