Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C89 ⋊ #1716 |
176 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=f,b^2=df,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^88,c^b=cf,h^c=h^88994 conjugacy classes — view the full character table.
| maximal subgroup of | #36468201, #1716×D89, C2×#26019886, … |
| maximal normal subgroup of | #36468201, #1716×D89, C2×#26019886, … |
| maximal quotient of | #36448210, #36454201, #36454215, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 4144);