Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | Q82×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3362 |
392 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 392 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=e,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^88,d^b=de,f^c=fg1135 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36543964, #36543973, #36543994, … |
| maximal normal subgroup of | #36543964, #36543973, #36543994, … |
| maximal quotient of | Q8×#15667936, #36571213, #36573364, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 17181);