Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C11×#117 ⋊ C2 |
| Sylow | C11 ⋊ #2485 |
540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=g,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^10238 conjugacy classes — view the full character table.
| maximal subgroup of | #14786732, #14786736, #14786769, … |
| maximal normal subgroup of | #14786732, #14786736, #14786769, … |
| maximal quotient of | #14675667, #14676309, #14676857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 8801);