Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C89 ⋊ #1340 |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=d,b^2=g,c^2=fg,e^2=g,f^2=g,b^a=bc,c^a=ce,f^a=fg,h^a=h^88,c^b=cf,d^b=defg,e^b=eg,f^b=fg,h^b=h^88,d^c=dg988 conjugacy classes — view the full character table.
| maximal subgroup of | #1340×D89, C2×#26018241, #36464575, … |
| maximal normal subgroup of | #1340×D89, C2×#26018241, #36464575, … |
| maximal quotient of | #36441108, #36441111, #36441120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 2499);