Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2597 |
454 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|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^881798 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2597×D89, C2×#26025797, #36725035, … |
| maximal normal subgroup of | #2597×D89, C2×#26025797, #36725035, … |
| maximal quotient of | #36476917, #36477040, #36478037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 10055);