Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×Q8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2984 |
364 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 179 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=f,b^2=e,c^2=e,f^2=g,b^a=be,d^a=de,c^b=ceg,h^b=h^88,h^d=h^881810 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36525614, #36525616, #36525622, … |
| maximal normal subgroup of | #36525614, #36525616, #36525622, … |
| maximal quotient of | #36553169, #36553490, #36553498, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 13598);