Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #2720 |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=e,b^2=ef,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^c=h^10172 conjugacy classes — view the full character table.
| maximal subgroup of | #14961203, #14961216, #14961241, … |
| maximal normal subgroup of | #14961203, #14961216, #14961241, … |
| maximal quotient of | #14681466, #14681648, #14681709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 11384);