Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | D4×Q8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3276 |
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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=g,c^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^88,c^b=cg,d^b=de,e^b=eg,e^d=eg,h^d=h^881129 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36543806, #36543808, #36543851, … |
| maximal normal subgroup of | #36543806, #36543808, #36543851, … |
| maximal quotient of | #36545741, #36545848, #36545955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 16156);