Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×C11×M16 ⋊ C2 |
| Sylow | C11 ⋊ #3055 |
548 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|b^2=e,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^10,d^b=dg232 conjugacy classes — view the full character table.
| maximal subgroup of | #14791196, #14791201, #14791218, … |
| maximal normal subgroup of | #14791196, #14791201, #14791218, … |
| maximal quotient of | #14736541, #14736563, #14736585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 14129);