Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #557×C89 ⋊ C2 |
| Sylow | C89 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D89 |
| commutator, socle, cosocle | C22×C89 | C25 |
| Fitting | #557×C89 | C2 |
| prime radical | C2×#13083575 | C22 |
| hypercenter | #557 | D89 |
| hypocenter | C89 | Q8×#41 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ #557 | |
1068 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^b=df,h^b=h^88,h^d=h^88,h^e=h^881150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36530407, #36530415, #36530422, … |
| maximal normal subgroup of | #36530407, #36530415, #36530422, … |
| maximal quotient of | C4⋊C4×#13083575, #36713745, #36713855, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 18092);