Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #391×C89 ⋊ C2 |
| Sylow | C89 ⋊ C4×#124 |
652 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 213 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=f,c^2=e,d^2=g,b^a=be,c^a=cf,h^b=h^88,h^c=h^88,h^d=h^881288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36442396, #36442469, #36442542, … |
| maximal normal subgroup of | #36442396, #36442469, #36442542, … |
| maximal quotient of | #36475583, #36475611, #391×Dic89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 7053);