Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C11×#126 ⋊ C2 |
| Sylow | C11 ⋊ #2601 |
518 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=e,d^2=g,b^a=be,c^a=cf,d^a=de,h^a=h^10,c^b=cg,h^c=h^10178 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2601, C2×#13074215, #14924463, … |
| maximal normal subgroup of | D11×#2601, C2×#13074215, #14924463, … |
| maximal quotient of | #14676303, #14676525, #14677851, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 10109);