Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #520×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3428 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D89 |
| commutator | C2×C89 | C24×C4 |
| Fitting | #520×C89 | C2 |
| socle, cosocle | C22×C89 | C25 |
| prime radical | C2×#41×D89 | C2 |
| hypercenter | #520 | D89 |
| hypocenter | C89 | #3428 |
| LCS | G ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ #520 | |
1540 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=g,e^2=f,b^a=bf,d^a=df,c^b=cf,h^d=h^88,h^e=h^881564 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36555294, #36555296, #36555312, … |
| maximal normal subgroup of | #36555294, #36555296, #36555312, … |
| maximal quotient of | #36712641, #36712653, #36712656, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 17710);