Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2663 |
498 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,89|b^2=eg,d^2=f,b^a=be,c^a=cf,c^b=cg,d^c=de,h^c=h^881792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36529377, #36529381, #36529407, … |
| maximal normal subgroup of | #36529377, #36529381, #36529407, … |
| maximal quotient of | #36480995, #36481010, #36481070, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 10658);