Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C11×SD16 ⋊ C2 |
| Sylow | C11 ⋊ #3173 |
362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^10172 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3173, C2×#13079229, #15623621, … |
| maximal normal subgroup of | D11×#3173, C2×#13079229, #15623621, … |
| maximal quotient of | #14754332, #14758032, #14758038, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 15123);