Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #2729 |
480 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=ef,b^2=e,d^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^10172 conjugacy classes — view the full character table.
| maximal subgroup of | #14961383, #14961388, #14961400, … |
| maximal normal subgroup of | #14961383, #14961388, #14961400, … |
| maximal quotient of | #14681558, #14681739, #14681786, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 11488);