Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #328×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1600 |
320 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,89|c^2=fg,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^88,d^b=df,e^b=eg,h^b=h^88,d^c=dg,h^c=h^88859 conjugacy classes — view the full character table.
| maximal subgroup of | #1600×D89, C2×#26019201, #36526638, … |
| maximal normal subgroup of | #1600×D89, C2×#26019201, #36526638, … |
| maximal quotient of | #36443144, #36443164, #36443174, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 3459);