Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #2297 |
936 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=eg,d^2=f,b^a=be,c^a=cf,h^a=h^10,h^b=h^10256 conjugacy classes — view the full character table.
| maximal subgroup of | #14647242, #14647245, #14647246, … |
| maximal normal subgroup of | #14647242, #14647245, #14647246, … |
| maximal quotient of | #14674888, #14674916, C4×#10622833, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7001);