Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C11×C4⋊Q8 ⋊ C2 |
| Sylow | C11 ⋊ #22117 |
836 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^8,11|a^2=g,b^2=gh,d^2=e,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,c^b=ceh,f^c=fh,i^c=i^10332 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 181686);