Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #496×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3217 |
490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,89|b^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,f^c=fg,h^d=h^88730 conjugacy classes — view the full character table.
| maximal subgroup of | #36535664, #36535668, #36535735, … |
| maximal normal subgroup of | #36535664, #36535668, #36535735, … |
| maximal quotient of | #36563776, #36564164, #36564988, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 15524);