Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ Q8×M16 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=e,c^2=ef,f^2=g,b^a=be,d^a=dg,h^a=h^5,d^c=dg,h^c=h^8,h^d=h^12,h^f=h^12110 conjugacy classes — view the full character table.
| maximal subgroup of | #16782643, #16782645, #16782651, … |
| maximal normal subgroup of | #16782643, #16782645, #16782651, … |
| maximal quotient of | C4⋊C4×#6118, #16797158, #16797468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21312);