Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | #382×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2328 |
740 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 197 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=g,b^2=eg,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,h^b=h^881276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36451124, #36451128, #36451152, … |
| maximal normal subgroup of | #36451124, #36451128, #36451152, … |
| maximal quotient of | #36475691, #36475735, #36475793, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 7233);