Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×#99×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1964 |
408 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 85 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=df,c^2=e,b^a=bd,c^a=ce,d^a=dg,d^b=dg,f^b=fg,h^c=h^881000 conjugacy classes — view the full character table.
| maximal subgroup of | #1964×D89, C2×#26021086, #36558174, … |
| maximal normal subgroup of | #1964×D89, C2×#26021086, #36558174, … |
| maximal quotient of | #36453250, #36453254, #36453258, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 5344);