Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×Q8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1588 |
166 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 65 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=e,b^2=f,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cfg,d^a=df,h^a=h^88,d^b=df1798 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1588×D89, C2×#26019130, #36523999, … |
| maximal normal subgroup of | #1588×D89, C2×#26019130, #36523999, … |
| maximal quotient of | #36445239, #36445292, #36445701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 3388);