Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#478 ⋊ C2 |
| Sylow | C11 ⋊ #3240 |
328 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|b^2=eg,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,h^b=h^10,f^c=fg,h^d=h^10121 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3240, C2×#13079855, #15625940, … |
| maximal normal subgroup of | D11×#3240, C2×#13079855, #15625940, … |
| maximal quotient of | #14763314, #14763517, #14764351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 15749);