Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C43 |
No aliases for this group.
| Fitting | #395×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2785 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D89 |
| commutator, socle, cosocle | C23×C89 | C24 |
| Fitting | #395×C89 | C2 |
| prime radical | C22×D356 | C22 |
| hypercenter | #395 | D89 |
| hypocenter | C89 | #2785 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #395 | |
428 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,89|a^2=g,b^2=f,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=def,h^a=h^88,c^b=cg,d^b=de,h^b=h^88,h^c=h^881000 conjugacy classes — view the full character table.
| maximal subgroup of | #36466786, #36466790, #36467372, … |
| maximal normal subgroup of | #36466786, #36466790, #36467372, … |
| maximal quotient of | #36482328, #36483243, #36484711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 12218);