Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C22⋊Q8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2681 |
618 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=f,b^2=e,c^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^88,c^b=cg,d^b=de,h^c=h^88,h^d=h^881264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36761372, #36761377, #36761398, … |
| maximal normal subgroup of | #36761372, #36761377, #36761398, … |
| maximal quotient of | #36481752, #36481760, #36481779, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 10865);