Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #2264 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|b^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,d^b=de,e^b=ef,f^b=fg,h^b=h^10136 conjugacy classes — view the full character table.
| maximal subgroup of | #14674388, #14674391, #14674451, … |
| maximal normal subgroup of | #14674388, #14674391, #14674451, … |
| maximal quotient of | #14674212, #14674219, #14674281, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6827);