Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C89 ⋊ #2987 |
314 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 197 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=e,c^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^88,c^b=ceg,d^b=dg1270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36448835, #36448838, #36449380, … |
| maximal normal subgroup of | #36448835, #36448838, #36449380, … |
| maximal quotient of | #36553192, #36553213, #36553528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 13616);