Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#126×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2860 |
516 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 149 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,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=dg,h^c=h^881276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36727374, #36727380, #36727397, … |
| maximal normal subgroup of | #36727374, #36727380, #36727397, … |
| maximal quotient of | #36485622, #36485683, #36485694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 12875);