Finite Group Databasebeta

← Group #231600

Character table — Group #231600

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444444444444444444488888888888844444444448888888888888888884444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ31111111111111111111111111-1-1-1-11-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111
χ5111111111111111111111-1-1-1-111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111
χ7111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1
χ91111111111111111-1-1-1-11111111111111111111111-1-1-1-11111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ101111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111
χ121111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111111111-1-1-1-111-1-1
χ131111111111111111-1-1-1-11-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-11111-1-11111-1-1-1-1
χ151111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ161111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ171-1-111-1-111111-1-1-1-1ii−i−i-1ii−i−iii−i−i111-1-11111-1-1-1-1i−ii−ii−ii−ii−i1-1ii−i−iii−i−iii−i−i11-1-11-11-11-11-1i−i
χ181-1-111-1-111111-1-1-1-1ii−i−i-1ii−i−iii−i−i111-1-1-1-1-1-11111−iii−ii−ii−i−ii1-1ii−i−i−i−iii−i−iii-1-111-11-111-11-1−ii
χ191-1-111-1-111111-1-1-1-1ii−i−i-1ii−i−i−i−iii1-1-1111111-1-1-1-1i−ii−ii−i−iii−i-11−i−iiiii−i−i−i−iii-1-1111-1-111-1-11−ii
χ201-1-111-1-111111-1-1-1-1ii−i−i-1ii−i−i−i−iii1-1-111-1-1-1-11111−iii−ii−i−ii−ii-11−i−iii−i−iiiii−i−i11-1-1-111-11-1-11i−i
χ211-1-111-1-111111-1-1-1-1ii−i−i-1−i−iiiii−i−i1-1-1111111-1-1-1-1i−ii−i−iii−ii−i-11−i−iii−i−iiiii−i−i-1-111-111-1-111-1−ii
χ221-1-111-1-111111-1-1-1-1ii−i−i-1−i−iiiii−i−i1-1-111-1-1-1-11111−iii−i−iii−i−ii-11−i−iiiii−i−i−i−iii11-1-11-1-11-111-1i−i
χ231-1-111-1-111111-1-1-1-1ii−i−i-1−i−iii−i−iii111-1-11111-1-1-1-1i−ii−i−ii−iii−i1-1ii−i−i−i−iii−i−iii11-1-1-11-11-11-11i−i
χ241-1-111-1-111111-1-1-1-1ii−i−i-1−i−iii−i−iii111-1-1-1-1-1-11111−iii−i−ii−ii−ii1-1ii−i−iii−i−iii−i−i-1-1111-11-1-11-11−ii
χ251-1-111-1-111111-1-1-1-1−i−iii-1ii−i−iii−i−i111-1-11111-1-1-1-1−ii−iii−ii−i−ii1-1−i−iiiii−i−iii−i−i11-1-1-11-11-11-11−ii
χ261-1-111-1-111111-1-1-1-1−i−iii-1ii−i−iii−i−i111-1-1-1-1-1-11111i−i−iii−ii−ii−i1-1−i−iii−i−iii−i−iii-1-1111-11-1-11-11i−i
χ271-1-111-1-111111-1-1-1-1−i−iii-1ii−i−i−i−iii1-1-1111111-1-1-1-1−ii−iii−i−ii−ii-11ii−i−iii−i−i−i−iii-1-111-111-1-111-1i−i
χ281-1-111-1-111111-1-1-1-1−i−iii-1ii−i−i−i−iii1-1-111-1-1-1-11111i−i−iii−i−iii−i-11ii−i−i−i−iiiii−i−i11-1-11-1-11-111-1−ii
χ291-1-111-1-111111-1-1-1-1−i−iii-1−i−iiiii−i−i1-1-1111111-1-1-1-1−ii−ii−iii−i−ii-11ii−i−i−i−iiiii−i−i-1-1111-1-111-1-11i−i
χ301-1-111-1-111111-1-1-1-1−i−iii-1−i−iiiii−i−i1-1-111-1-1-1-11111i−i−ii−iii−ii−i-11ii−i−iii−i−i−i−iii11-1-1-111-11-1-11−ii
χ311-1-111-1-111111-1-1-1-1−i−iii-1−i−iii−i−iii111-1-11111-1-1-1-1−ii−ii−ii−ii−ii1-1−i−iii−i−iii−i−iii11-1-11-11-11-11-1−ii
χ321-1-111-1-111111-1-1-1-1−i−iii-1−i−iii−i−iii111-1-1-1-1-1-11111i−i−ii−ii−iii−i1-1−i−iiiii−i−iii−i−i-1-111-11-111-11-1i−i
χ332222222222-2-222-2-22222-200000000-2000022-2-222-2-222-2-20000-2-20000000000000000000000000000
χ342222222222-2-222-2-22222-200000000-20000-2-222-2-222-2-2-2-20000220000000000000000000000000000
χ352222222222-2-222-2-2-2-2-2-2-200000000-2000022-2-222-2-2-2-2220000220000000000000000000000000000
χ362222222222-2-222-2-2-2-2-2-2-200000000-20000-2-222-2-22222220000-2-20000000000000000000000000000
χ3722222222-2-222-2-2220000-222222222-22222000000000000-2-2-2-200-2-200000000000000000000000000
χ3822222222-2-222-2-2220000-22222-2-2-2-2-2-2-2-2-2000000000000-2-222002200000000000000000000000000
χ3922222222-2-222-2-2220000-2-2-2-2-22222-2-2-2-2-200000000000022-2-2002200000000000000000000000000
χ4022222222-2-222-2-2220000-2-2-2-2-2-2-2-2-2-22222000000000000222200-2-200000000000000000000000000
χ4122-2-2-22-22002-2002-2000002-22-22-22-202-22-2i2−i2i2−i2i2−i2i2−i20000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000
χ4222-2-2-22-22002-2002-2000002-22-22-22-202-22-2−i2i2−i2i2−i2i2−i2i20000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000
χ4322-2-2-22-22002-2002-2000002-22-2-22-220-22-22i2−i2i2−i2i2−i2i2−i20000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000
χ4422-2-2-22-22002-2002-2000002-22-2-22-220-22-22−i2i2−i2i2−i2i2−i2i20000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000
χ4522-2-2-22-22002-2002-200000-22-222-22-20-22-22i2−i2i2−i2i2−i2i2−i20000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ4622-2-2-22-22002-2002-200000-22-222-22-20-22-22−i2i2−i2i2−i2i2−i2i20000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ4722-2-2-22-22002-2002-200000-22-22-22-2202-22-2i2−i2i2−i2i2−i2i2−i20000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ4822-2-2-22-22002-2002-200000-22-22-22-2202-22-2−i2i2−i2i2−i2i2−i2i20000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ492-22-2-2-222002-200-22000002i−2i−2i2i2i−2i−2i2i02-2-22i2−i2i2−i2−i2i2−i2i20000000000000000−222−2−222−2i2−i2−i2i20000000000
χ502-22-2-2-222002-200-22000002i−2i−2i2i2i−2i−2i2i02-2-22−i2i2−i2i2i2−i2i2−i200000000000000002−2−222−2−22−i2i2i2−i20000000000
χ512-22-2-2-222002-200-22000002i−2i−2i2i−2i2i2i−2i0-222-2i2−i2i2−i2−i2i2−i2i20000000000000000−222−22−2−22−i2i2i2−i20000000000
χ522-22-2-2-222002-200-22000002i−2i−2i2i−2i2i2i−2i0-222-2−i2i2−i2i2i2−i2i2−i200000000000000002−2−22−222−2i2−i2−i2i20000000000
χ532-22-2-2-222002-200-2200000−2i2i2i−2i2i−2i−2i2i0-222-2i2−i2i2−i2−i2i2−i2i200000000000000002−2−22−222−2−i2i2i2−i20000000000
χ542-22-2-2-222002-200-2200000−2i2i2i−2i2i−2i−2i2i0-222-2−i2i2−i2i2i2−i2i2−i20000000000000000−222−22−2−22i2−i2−i2i20000000000
χ552-22-2-2-222002-200-2200000−2i2i2i−2i−2i2i2i−2i02-2-22i2−i2i2−i2−i2i2−i2i200000000000000002−2−222−2−22i2−i2−i2i20000000000
χ562-22-2-2-222002-200-2200000−2i2i2i−2i−2i2i2i−2i02-2-22−i2i2−i2i2i2−i2i2−i20000000000000000−222−2−222−2−i2i2i2−i20000000000
χ572-2-222-2-2222-2-2-2-2222i2i−2i−2i200000000-2000022-2-2-2-2222i−2i−2i2i0000−2i2i0000000000000000000000000000
χ582-2-222-2-2222-2-2-2-2222i2i−2i−2i200000000-20000-2-22222-2-2−2i2i−2i2i00002i−2i0000000000000000000000000000
χ592-2-222-2-2222-2-2-2-222−2i−2i2i2i200000000-2000022-2-2-2-222−2i2i2i−2i00002i−2i0000000000000000000000000000
χ602-2-222-2-2222-2-2-2-222−2i−2i2i2i200000000-20000-2-22222-2-22i−2i2i−2i0000−2i2i0000000000000000000000000000
χ612-2-222-2-22-2-22222-2-2000022i2i−2i−2i2i2i−2i−2i-222-2-2000000000000−2i2i−2i2i00-2200000000000000000000000000
χ622-2-222-2-22-2-22222-2-2000022i2i−2i−2i−2i−2i2i2i-2-2-222000000000000−2i2i2i−2i002-200000000000000000000000000
χ632-2-222-2-22-2-22222-2-200002−2i−2i2i2i2i2i−2i−2i-2-2-2220000000000002i−2i−2i2i002-200000000000000000000000000
χ642-2-222-2-22-2-22222-2-200002−2i−2i2i2i−2i−2i2i2i-222-2-20000000000002i−2i2i−2i00-2200000000000000000000000000
χ6544444444-4-4-4-4-4-4-4-40000400000000400000000000000000000000000000000000000000000000000
χ664444-4-4-4-44-4004-4000000000000000000000000000000000000000022−2222−220000000000000000000000
χ674444-4-4-4-44-4004-40000000000000000000000000000000000000000−2222−22220000000000000000000000
χ684444-4-4-4-4-4400-44004-44-4000000000000000000000000000000000000000000000000000000000000
χ694444-4-4-4-4-4400-4400-44-44000000000000000000000000000000000000000000000000000000000000
χ7044-4-4-44-4400-4400-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ7144-4-4-44-4400-4400-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ724-44-4-4-44400-44004-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ734-44-4-4-44400-44004-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ744-4-444-4-44-4-4-4-444440000-400000000400000000000000000000000000000000000000000000000000
χ754-4-44-444-44-400-4400000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ764-4-44-444-44-400-440000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ774-4-44-444-4-44004-4004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ784-4-44-444-4-44004-400−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ7988-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000
χ808-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000000000

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