Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C89 ⋊ #3502 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D89 |
| commutator, socle, cosocle | C22×C89 | C25 |
| Fitting | #544×C89 | C2 |
| prime radical | C23×C89 | C24 |
| hypercenter | #544 | D89 |
| hypocenter | C89 | #3502 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ #544 | |
964 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=g,b^2=f,c^2=g,d^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^c=h^88,h^d=h^881012 conjugacy classes — view the full character table.
| maximal subgroup of | #36527279, #36527283, #36527286, … |
| maximal normal subgroup of | #36527279, #36527283, #36527286, … |
| maximal quotient of | #36714524, #36714863, #36714867, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 18318);