Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C89 ⋊ #2332 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D89 |
| commutator | C22×C89 | C23×C4 |
| Fitting | #381×C89 | C2 |
| socle, cosocle | C23×C89 | C24 |
| prime radical | C24×C89 | C23 |
| hypercenter | #381 | D89 |
| hypocenter | C89 | #2332 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #381 | |
484 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 177 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=g,d^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,h^b=h^881276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36452481, #36452485, #36452495, … |
| maximal normal subgroup of | #36452481, #36452485, #36452495, … |
| maximal quotient of | #36475695, #36475750, #36475778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 7263);