Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×C11×C22⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ #2597 |
454 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=eg,b^2=fg,c^2=g,d^2=ef,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 | D11×#2597, C2×#13074161, #14924380, … |
| maximal normal subgroup of | D11×#2597, C2×#13074161, #14924380, … |
| maximal quotient of | #14676262, #14676385, #14677382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 10055);