Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×SD16×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2019 |
362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,89|a^2=g,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cf,d^b=dg,f^b=fg,h^b=h^88,d^c=dg,e^c=eg,f^c=fg1258 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2019×D89, C2×#26021364, #36581632, … |
| maximal normal subgroup of | #2019×D89, C2×#26021364, #36581632, … |
| maximal quotient of | #36455031, #36455048, #36455098, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 5622);