Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #382×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2317 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D89 |
| commutator | C22×C89 | C23×C4 |
| Fitting | #382×C89 | C2 |
| socle, cosocle | C23×C89 | C24 |
| prime radical | C23×D89 | C23 |
| hypercenter | #382 | D89 |
| hypocenter | C89 | #2317 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #382 | |
600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^88,c^b=ce,h^b=h^881276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36463587, #36463591, #36463833, … |
| maximal normal subgroup of | #36463587, #36463591, #36463833, … |
| maximal quotient of | #36475689, #36475691, #36475712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 7135);