Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4×D4×C11 ⋊ C2 |
| Sylow | C11 ⋊ #2602 |
582 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,d^2=eg,b^a=be,c^a=cf,d^a=de,h^a=h^10,c^b=cg238 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2602, C2×#13074228, #14925181, … |
| maximal normal subgroup of | D11×#2602, C2×#13074228, #14925181, … |
| maximal quotient of | #14676318, #14676439, #14677909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 10122);