Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #2342 |
792 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=f,b^a=be,c^a=cf,h^a=h^10,d^b=de250 conjugacy classes — view the full character table.
| maximal subgroup of | #14769100, #14769106, #14769908, … |
| maximal normal subgroup of | #14769100, #14769106, #14769908, … |
| maximal quotient of | C22⋊C4×C22⋊Dic11, #14675180, #14675204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7359);