Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C22⋊C4×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2405 |
1116 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,89|c^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^88,c^b=cg1798 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36452330, #36452332, #36452340, … |
| maximal normal subgroup of | #36452330, #36452332, #36452340, … |
| maximal quotient of | #36476294, #36476312, #36477209, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 7837);