Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C82×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1711 |
178 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|b^2=dfg,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^882854 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1711×D89, C2×#26019864, #36542112, … |
| maximal normal subgroup of | #1711×D89, C2×#26019864, #36542112, … |
| maximal quotient of | #36448207, #36454173, #36454180, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 4122);