Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C89 ⋊ #1589 |
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^88,c^b=cg,d^b=df,h^c=h^881276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36466324, #36466326, #36466338, … |
| maximal normal subgroup of | #36466324, #36466326, #36466338, … |
| maximal quotient of | #36445249, #36445664, #36448369, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 3395);