Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#452 ⋊ C2 |
| Sylow | C11 ⋊ #3282 |
504 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,h^b=h^10,h^c=h^10,e^d=eg130 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3282, C2×#13080321, #15629061, … |
| maximal normal subgroup of | D11×#3282, C2×#13080321, #15629061, … |
| maximal quotient of | #14743593, #14743608, #14743623, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16215);