Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C11×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C11 ⋊ #3272 |
546 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|e^2=g,b^a=be,c^a=cf,e^a=eg,c^b=cg,d^b=de,e^b=eg,h^c=h^10,e^d=eg139 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3272, C2×#13080210, #15628948, … |
| maximal normal subgroup of | D11×#3272, C2×#13080210, #15628948, … |
| maximal quotient of | #14745034, #14745111, #14745117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16104);