Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C89 ⋊ #1426 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=d,b^2=cef,c^2=efg,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^88,d^b=dg1786 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1426×D89, C2×#26018458, #36474947, … |
| maximal normal subgroup of | #1426×D89, C2×#26018458, #36474947, … |
| maximal quotient of | #36442111, #36442136, C2×#26018458 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 2716);