Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #388×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2321 |
808 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=g,b^2=g,b^a=be,c^a=cf,d^a=de,h^a=h^88,c^b=ce,h^b=h^88,h^d=h^881276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2321×D89, C2×#26022914, #36713188, … |
| maximal normal subgroup of | #2321×D89, C2×#26022914, #36713188, … |
| maximal quotient of | #36475665, #36475709, #36475724, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 7172);