Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C89 ⋊ #1350 |
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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=g,c^2=fg,d^2=g,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,c^b=cf,d^b=defg,e^b=eg,f^b=fg,h^b=h^881261 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1350×D89, C2×#26018269, #36464679, … |
| maximal normal subgroup of | #1350×D89, C2×#26018269, #36464679, … |
| maximal quotient of | #36441115, #36441118, #36441127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 2527);