Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C89 ⋊ #2035 |
316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 87 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,c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^88,c^b=cf,e^c=eg1264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2035×D89, C2×#26021448, #36581904, … |
| maximal normal subgroup of | #2035×D89, C2×#26021448, #36581904, … |
| maximal quotient of | #36457724, #36457745, #36457814, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 5706);