Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | B(4,𝔽2)×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2199 |
270 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 41 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^a=bd,c^a=ce,f^a=fg,c^b=cg,e^b=efg,d^c=df,h^c=h^88,e^d=eg721 conjugacy classes — view the full character table.
| maximal subgroup of | #2199×D89, C2×#26022251, #36708475, … |
| maximal normal subgroup of | #2199×D89, C2×#26022251, #36708475, … |
| maximal quotient of | #36466472, #36466473, #36466513, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 6509);