Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #385×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2342 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D89 |
| commutator | C22×C89 | C23×C4 |
| Fitting | #385×C89 | C2 |
| socle, cosocle | C23×C89 | C24 |
| prime radical | C24×D89 | C22 |
| hypercenter | #385 | D89 |
| hypocenter | C89 | #2342 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #385 | |
792 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=g,b^2=f,b^a=be,c^a=cf,d^b=de,h^b=h^88,h^c=h^881282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2342×D89, C2×#26023099, #36713698, … |
| maximal normal subgroup of | #2342×D89, C2×#26023099, #36713698, … |
| maximal quotient of | #36475827, #36475834, #36475858, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 7357);