Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C4⋊Q8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2432 |
836 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 173 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=e,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^881270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36471979, #36585828, #36585829, … |
| maximal normal subgroup of | #36471979, #36585828, #36585829, … |
| maximal quotient of | #36476401, #36476947, #36477307, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 8135);