Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×D4×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3339 |
366 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=eg,b^2=g,c^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^88,d^b=de,f^c=fg,h^c=h^881795 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36711288, #36711290, #36711340, … |
| maximal normal subgroup of | #36711288, #36711290, #36711340, … |
| maximal quotient of | #36570681, #36572078, #36572094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 16913);