Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #390×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2358 |
928 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 209 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=g,b^a=be,c^a=cf,d^b=de,h^b=h^88,h^c=h^88,h^d=h^881282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36471180, #36471184, #36471687, … |
| maximal normal subgroup of | #36471180, #36471184, #36471687, … |
| maximal quotient of | #36475829, #36475922, #36475941, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 7491);