Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #379×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1889 |
578 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 83 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=f,b^2=df,b^a=bd,c^a=ce,e^a=eg,e^b=eg,d^c=dg,f^c=fg,h^c=h^881264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1889×D89, C2×#26020657, #36556049, … |
| maximal normal subgroup of | #1889×D89, C2×#26020657, #36556049, … |
| maximal quotient of | #36449110, #36449120, #36449394, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 4915);