Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C4⋊Q8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3152 |
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 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=g,b^2=e,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,h^b=h^881264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36451942, #36451985, #36451987, … |
| maximal normal subgroup of | #36451942, #36451985, #36451987, … |
| maximal quotient of | #36542278, #36542322, #36542363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 14967);