Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C82×C11 ⋊ C2 |
| Sylow | C11 ⋊ #1335 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^7,11|a^2=d,c^2=eg,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^10,c^b=ce,e^b=eg,h^b=h^10364 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1335, C2×#13066590, #14663558, … |
| maximal normal subgroup of | D11×#1335, C2×#13066590, #14663558, … |
| maximal quotient of | #14640423, #14640426, #14640441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2484);