Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×D8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3334 |
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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,c^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^88,d^b=de,h^b=h^88,f^c=fg,h^d=h^881267 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36468019, #36468023, #36468047, … |
| maximal normal subgroup of | #36468019, #36468023, #36468047, … |
| maximal quotient of | #36570644, #36572068, #107×D356, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 16859);