Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #519×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1888 |
344 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 93 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=dfg,c^2=g,d^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^88,d^b=dg,e^b=eg,f^b=fg,d^c=dg,f^c=fg1528 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36470304, #36470309, #36470312, … |
| maximal normal subgroup of | #36470304, #36470309, #36470312, … |
| maximal quotient of | #36449088, #36449108, #36449362, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 4913);