Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| 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,h^a=h^10,c^b=ceg,d^b=dg178 conjugacy classes — view the full character table.
| maximal subgroup of | #14648161, #14648165, #14648168, … |
| maximal normal subgroup of | #14648161, #14648165, #14648168, … |
| maximal quotient of | #14752621, #14752654, #14752756, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13680);