Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#423 ⋊ C2 |
| Sylow | C11 ⋊ #2995 |
346 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,c^b=ceg,d^b=dg,h^b=h^10178 conjugacy classes — view the full character table.
| maximal subgroup of | #14648160, #14648164, #14648167, … |
| maximal normal subgroup of | #14648160, #14648164, #14648167, … |
| maximal quotient of | #14752620, #14752648, #14752751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13677);