Finite Group Databasebeta

← Group #209807

Character table — Group #209807

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111122222222222244444444444444448888888888888888888888888888888888881616161616161616
order12222222444444444444444444444444444422222244444444444444888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ51111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1211111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ171-11-111-1-1ii−i−i11-1-111-1-1i−i11-1-1i−ii−iii−i−i1-111-1-11-11-1i−i1-1i−iii−i−ii−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i
χ181-11-111-1-1ii−i−i11-1-111-1-1i−i11-1-1i−ii−iii−i−i1-111-1-11-11-1i−i1-1i−iii−i−ii−i-1-111−i−iii-1-111−i−iii-11−ii-11−ii
χ191-11-111-1-1ii−i−i11-1-111-1-1i−i11-1-1i−ii−iii−i−i1-1-1-111-111-1i−i-11−ii−i−iii−ii11-1-1ii−i−i-1-111−i−iii1-1i−i-11−ii
χ201-11-111-1-1ii−i−i11-1-111-1-1i−i11-1-1i−ii−iii−i−i1-1-1-111-111-1i−i-11−ii−i−iii−ii-1-111−i−iii11-1-1ii−i−i-11−ii1-1i−i
χ211-11-111-1-1ii−i−i11-1-111-1-1i−i-1-111i−ii−i−i−iii1-111-1-1-11-11−ii-11−iiii−i−i−ii11-1-1ii−i−i-1-111−i−iii-11−ii1-1i−i
χ221-11-111-1-1ii−i−i11-1-111-1-1i−i-1-111i−ii−i−i−iii1-111-1-1-11-11−ii-11−iiii−i−i−ii-1-111−i−iii11-1-1ii−i−i1-1i−i-11−ii
χ231-11-111-1-1ii−i−i11-1-111-1-1i−i-1-111i−ii−i−i−iii1-1-1-1111-1-11−ii1-1i−i−i−iiii−i11-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii
χ241-11-111-1-1ii−i−i11-1-111-1-1i−i-1-111i−ii−i−i−iii1-1-1-1111-1-11−ii1-1i−i−i−iiii−i-1-111−i−iii-1-111−i−iii1-1i−i1-1i−i
χ251-11-111-1-1−i−iii11-1-111-1-1−ii11-1-1−ii−ii−i−iii1-111-1-11-11-1−ii1-1−ii−i−iii−ii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii
χ261-11-111-1-1−i−iii11-1-111-1-1−ii11-1-1−ii−ii−i−iii1-111-1-11-11-1−ii1-1−ii−i−iii−ii-1-111ii−i−i-1-111ii−i−i-11i−i-11i−i
χ271-11-111-1-1−i−iii11-1-111-1-1−ii11-1-1−ii−ii−i−iii1-1-1-111-111-1−ii-11i−iii−i−ii−i11-1-1−i−iii-1-111ii−i−i1-1−ii-11i−i
χ281-11-111-1-1−i−iii11-1-111-1-1−ii11-1-1−ii−ii−i−iii1-1-1-111-111-1−ii-11i−iii−i−ii−i-1-111ii−i−i11-1-1−i−iii-11i−i1-1−ii
χ291-11-111-1-1−i−iii11-1-111-1-1−ii-1-111−ii−iiii−i−i1-111-1-1-11-11i−i-11i−i−i−iiii−i11-1-1−i−iii-1-111ii−i−i-11i−i1-1−ii
χ301-11-111-1-1−i−iii11-1-111-1-1−ii-1-111−ii−iiii−i−i1-111-1-1-11-11i−i-11i−i−i−iiii−i-1-111ii−i−i11-1-1−i−iii1-1−ii-11i−i
χ311-11-111-1-1−i−iii11-1-111-1-1−ii-1-111−ii−iiii−i−i1-1-1-1111-1-11i−i1-1−iiii−i−i−ii11-1-1−i−iii11-1-1−i−iii-11i−i-11i−i
χ321-11-111-1-1−i−iii11-1-111-1-1−ii-1-111−ii−iiii−i−i1-1-1-1111-1-11i−i1-1−iiii−i−i−ii-1-111ii−i−i-1-111ii−i−i1-1−ii1-1−ii
χ332222222222222-22-22-22-2222222-2-2-2-2-2-2-2-2-2-2000000-2-2220000000000000000000000000000000000
χ342222222222222-22-22-22-222-2-2-2-2-2-2-2-22222-2-200000022-2-20000000000000000000000000000000000
χ35222222222222-22-22-22-22-2-2000022-2-20000-2-20000220000-2-2-2-2000022000000000000000000000000
χ36222222222222-22-22-22-22-2-2000022-2-20000-2-20000-2-2000022220000-2-2000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-20000-2-2220000222-22-200000000002-22-200000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-20000-2-222000022-22-220000000000-22-2200000000000000000000000000
χ3922222222-2-2-2-22-22-22-22-2-2-2222222222222-2-2000000-2-2-2-20000000000000000000000000000000000
χ4022222222-2-2-2-22-22-22-22-2-2-2-2-2-2-22222-2-2-2-2-2-200000022220000000000000000000000000000000000
χ4122222222-2-2-2-2-22-22-22-22220000-2-2220000-2-20000220000-2-2220000-2-2000000000000000000000000
χ4222222222-2-2-2-2-22-22-22-22220000-2-2220000-2-20000-2-2000022-2-2000022000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-222000022-2-20000222-22-20000000000-22-2200000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-222000022-2-2000022-22-2200000000002-22-200000000000000000000000000
χ452-22-222-2-22i2i−2i−2i2-2-222-2-222i−2i22-2-2−2i2i−2i2i−2i−2i2i2i-22000000-222i−2i0000000000000000000000000000000000
χ462-22-222-2-22i2i−2i−2i2-2-222-2-222i−2i-2-222−2i2i−2i2i2i2i−2i−2i-220000002-2−2i2i0000000000000000000000000000000000
χ472-22-222-2-22i2i−2i−2i-222-2-222-2−2i2i00002i−2i−2i2i0000-2200002-20000-22−2i2i00002i−2i000000000000000000000000
χ482-22-222-2-22i2i−2i−2i-222-2-222-2−2i2i00002i−2i−2i2i0000-220000-2200002-22i−2i0000−2i2i000000000000000000000000
χ492-22-222-2-22i2i−2i−2i-2-222-2-222−2i2i0000−2i2i2i−2i00002-22-2-2200000000002i−2i−2i2i00000000000000000000000000
χ502-22-222-2-22i2i−2i−2i-2-222-2-222−2i2i0000−2i2i2i−2i00002-2-222-20000000000−2i2i2i−2i00000000000000000000000000
χ512-22-222-2-2−2i−2i2i2i2-2-222-2-22−2i2i22-2-22i−2i2i−2i2i2i−2i−2i-22000000-22−2i2i0000000000000000000000000000000000
χ522-22-222-2-2−2i−2i2i2i2-2-222-2-22−2i2i-2-2222i−2i2i−2i−2i−2i2i2i-220000002-22i−2i0000000000000000000000000000000000
χ532-22-222-2-2−2i−2i2i2i-222-2-222-22i−2i0000−2i2i2i−2i0000-2200002-20000-222i−2i0000−2i2i000000000000000000000000
χ542-22-222-2-2−2i−2i2i2i-222-2-222-22i−2i0000−2i2i2i−2i0000-220000-2200002-2−2i2i00002i−2i000000000000000000000000
χ552-22-222-2-2−2i−2i2i2i-2-222-2-2222i−2i00002i−2i−2i2i00002-22-2-220000000000−2i2i2i−2i00000000000000000000000000
χ562-22-222-2-2−2i−2i2i2i-2-222-2-2222i−2i00002i−2i−2i2i00002-2-222-200000000002i−2i−2i2i00000000000000000000000000
χ57444-4-4-4-444-44-400000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ58444-4-4-4-444-44-40000000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ59444-4-4-4-44-44-4400000000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ60444-4-4-4-44-44-440000000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ6144-444-4-4-400004040-40-40004-44-4000000000000000000000000000000000000000000000000000000
χ6244-444-4-4-400004040-40-4000-44-44000000000000000000000000000000000000000000000000000000
χ6344-444-4-4-40000-40-40404000000000004i−4i4i−4i0000000000000000000000000000000000000000000000
χ6444-444-4-4-40000-40-4040400000000000−4i4i−4i4i0000000000000000000000000000000000000000000000
χ6544-4-4-444-40000040-40-4040000000000000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ6644-4-4-444-40000040-40-404000000000000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ6744-4-4-444-400000-404040-400000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ6844-4-4-444-400000-404040-40000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ694-444-4-44-44i−4i−4i4i00000000000000000000000000000000000000000000000000002i−2i−2i2i-222-200000000
χ704-444-4-44-44i−4i−4i4i0000000000000000000000000000000000000000000000000000−2i2i2i−2i2-2-2200000000
χ714-444-4-44-4−4i4i4i−4i00000000000000000000000000000000000000000000000000002i−2i−2i2i2-2-2200000000
χ724-444-4-44-4−4i4i4i−4i0000000000000000000000000000000000000000000000000000−2i2i2i−2i-222-200000000
χ734-4-44-44-44000004040-40-40000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ744-4-44-44-44000004040-40-4000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ754-4-44-44-4400000-40-40404000000000000000000000000000000000000000022−22−22220000000000000000
χ764-4-44-44-4400000-40-404040000000000000000000000000000000000000000−222222−220000000000000000
χ774-4-4-44-444000040-40-4040004-4-44000000000000000000000000000000000000000000000000000000
χ784-4-4-44-444000040-40-404000-444-4000000000000000000000000000000000000000000000000000000
χ794-4-4-44-4440000-404040-4000000000004-4-440000000000000000000000000000000000000000000000
χ804-4-4-44-4440000-404040-400000000000-444-40000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).