Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #500×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1693 |
166 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 55 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=df,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,c^b=cf,e^c=eg,h^c=h^88991 conjugacy classes — view the full character table.
| maximal subgroup of | #36468275, #36468277, #36468282, … |
| maximal normal subgroup of | #36468275, #36468277, #36468282, … |
| maximal quotient of | #36447519, #36450640, #36452822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 4020);