Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #554×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D89 |
| commutator, socle, cosocle | C22×C89 | C25 |
| Fitting | #554×C89 | C2 |
| hypercenter | #554 | D89 |
| hypocenter | C89 | #3519 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ #554 | |
1252 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|e^2=fg,b^a=bf,c^a=cg,e^a=ef,h^a=h^88,d^b=df,h^c=h^88,h^e=h^881144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36530873, #36530884, #36530961, … |
| maximal normal subgroup of | #36530873, #36530884, #36530961, … |
| maximal quotient of | #36714636, #36715146, #36715189, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 18543);