Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #520×C89 ⋊ C2 |
| Sylow | C89 ⋊ C4×H(5,𝔽2) |
1660 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=g,e^2=g,b^a=bf,d^a=df,c^b=cf,h^d=h^88,h^e=h^881564 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36560299, #36560305, #36560310, … |
| maximal normal subgroup of | #36560299, #36560305, #36560310, … |
| maximal quotient of | #36712660, #36712662, #36712666, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 17716);