Finite Group DatabasebetaFinite Group Databasebeta| order | 22336 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C349 ⋊ C8×Q8 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22336 |
Polycyclic presentation:
2^6,349|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,g^a=g^136,g^c=g^213,g^e=g^348910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22336, 1598);