Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #448×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3211 |
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 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=ce,h^b=h^88,f^c=fg,h^c=h^88868 conjugacy classes — view the full character table.
| maximal subgroup of | #36528447, #36528449, #36528458, … |
| maximal normal subgroup of | #36528447, #36528449, #36528458, … |
| maximal quotient of | #36563752, #36564114, #36564953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 15474);