Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #2574 |
436 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=eg,b^2=eg,c^2=e,d^2=f,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×#2574, C2×#13073890, #14924127, … |
| maximal normal subgroup of | D11×#2574, C2×#13073890, #14924127, … |
| maximal quotient of | #14676099, #14676202, #14676751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 9784);