Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C22⋊Q8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2626 |
668 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 157 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=f,c^2=f,b^a=be,c^a=cf,c^b=cg,h^b=h^88,d^c=de1264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36450468, #36450478, #36454677, … |
| maximal normal subgroup of | #36450468, #36450478, #36454677, … |
| maximal quotient of | #36480840, #36480862, #36480970, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 10317);