Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C11×#135 ⋊ C2 |
| Sylow | C11 ⋊ #3002 |
764 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,h^c=h^10178 conjugacy classes — view the full character table.
| maximal subgroup of | #14759606, #14759613, #14759617, … |
| maximal normal subgroup of | #14759606, #14759613, #14759617, … |
| maximal quotient of | #14725875, #14725926, #14725977, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13724);