Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #3123 |
394 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,f^c=fg,h^d=h^10127 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3123, C2×#13078862, #15622132, … |
| maximal normal subgroup of | D11×#3123, C2×#13078862, #15622132, … |
| maximal quotient of | #14753858, #14756846, #14756854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 14756);