Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C8×D4×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3294 |
494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^88,d^b=de,f^c=fg,h^c=h^881795 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36543770, #36543777, #36543807, … |
| maximal normal subgroup of | #36543770, #36543777, #36543807, … |
| maximal quotient of | D4×#15667934, #36570643, #36571572, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 16324);