Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #322×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1722 |
198 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=f,b^2=d,c^2=eg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^88,c^b=cf1786 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36467848, #1722×D89, C2×#26019923, … |
| maximal normal subgroup of | #36467848, #1722×D89, C2×#26019923, … |
| maximal quotient of | #36448217, #36454228, #36454235, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 4181);