Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#491 ⋊ C2 |
| Sylow | C11 ⋊ #3320 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=eg,b^2=g,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,h^b=h^10,f^c=fg,h^c=h^10,h^d=h^10109 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3320, C2×#13080786, #15630544, … |
| maximal normal subgroup of | D11×#3320, C2×#13080786, #15630544, … |
| maximal quotient of | #14769342, #14770090, #14770880, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16680);