Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #396×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2609 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D89 |
| commutator, socle, cosocle | C23×C89 | C24 |
| Fitting | #396×C89 | C2 |
| prime radical | C22×C22⋊D89 | C22 |
| hypercenter | #396 | D89 |
| hypocenter | C89 | #2609 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #396 | |
540 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|b^2=eg,d^2=g,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^88,h^d=h^881006 conjugacy classes — view the full character table.
| maximal subgroup of | #2609×D89, C2×#26025925, #36725299, … |
| maximal normal subgroup of | #2609×D89, C2×#26025925, #36725299, … |
| maximal quotient of | #36477119, #36477121, #36478377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 10183);