Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #537×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3492 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D89 |
| commutator, socle, cosocle | C22×C89 | C25 |
| Fitting | #537×C89 | C2 |
| hypercenter | #537 | D89 |
| hypocenter | C89 | #3492 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ #537 | |
1124 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|b^2=g,d^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^88,h^c=h^881012 conjugacy classes — view the full character table.
| maximal subgroup of | #36527071, #36527079, #36527132, … |
| maximal normal subgroup of | #36527071, #36527079, #36527132, … |
| maximal quotient of | #36714488, #36714714, #36714915, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 18217);