Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C89 ⋊ #1386 |
140 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 140 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=d,b^2=e,c^2=fg,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^88,c^b=cg,h^b=h^881264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1386×D89, C2×#26018359, #36469345, … |
| maximal normal subgroup of | #1386×D89, C2×#26018359, #36469345, … |
| maximal quotient of | #36441307, #36441356, #36441363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 2617);