Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C22⋊Q8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2472 |
786 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|b^2=f,c^2=e,d^2=f,b^a=be,c^a=cf,d^a=de,h^a=h^88,c^b=cg,h^b=h^88,h^c=h^88,h^d=h^881270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2472×D89, C2×#26024385, #36722214, … |
| maximal normal subgroup of | #2472×D89, C2×#26024385, #36722214, … |
| maximal quotient of | #36476349, #36476582, #36477420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 8643);