Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C11×#386 ⋊ C2 |
| Sylow | C11 ⋊ #2308 |
1160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=g,b^a=be,c^a=cf,d^a=de,c^b=ce,h^d=h^10184 conjugacy classes — view the full character table.
| maximal subgroup of | #14668718, #14670018, #14753038, … |
| maximal normal subgroup of | #14668718, #14670018, #14753038, … |
| maximal quotient of | #14675010, #14675015, #14675070, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7084);