Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×#126×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D89 |
| commutator, socle, cosocle | C22×C89 | C25 |
| Fitting | C2×#126×C89 | C2 |
| prime radical | #19152186 | C2 |
| hypercenter | C2×#126 | D89 |
| hypocenter | C89 | #3564 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ C2×#126 | |
936 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=g,c^2=f,d^2=fg,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^88,c^b=cg,d^b=df1270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36446774, #36446778, #36527880, … |
| maximal normal subgroup of | #36446774, #36446778, #36527880, … |
| maximal quotient of | #36717421, #36717540, #36717716, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 19134);