Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C11×#385 ⋊ C2 |
| Sylow | C11 ⋊ #2337 |
540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=eg,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,h^a=h^10,c^b=ce,h^d=h^10184 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2337, C2×#13071430, #14912699, … |
| maximal normal subgroup of | D11×#2337, C2×#13071430, #14912699, … |
| maximal quotient of | #14675044, #14675105, #14675109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7324);