Finite Group Databasebeta

← Group #226142

Character table — Group #226142

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444442222444444444488888888888844444444448888888888888888884444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ31111111111111111111111111-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111
χ7111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-111-1-1
χ91111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ111111111111111111-1-1-1-111111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ121111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-11-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-111111111-1-1-1-1-1-1
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
χ161111111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-111-1-111-1-111
χ171-1111-1-1-1-1-1-11111-111-1-1-1ii−i−iii−i−i11111-1-1-1-111-1-1i−i1-111-1-1i−i1-111-1-1ii−i−iii−i−i11-1-1i−ii−ii−ii−i1-1
χ181-1111-1-1-1-1-1-11111-111-1-1-1ii−i−iii−i−i1-1-1-1-1111111-1-1i−i1-1-1-111i−i1-111-1-1−i−iii−i−iii-1-111i−i−iii−i−ii-11
χ191-1111-1-1-1-1-1-11111-111-1-1-1ii−i−i−i−iii11111-1-1-1-1-1-111i−i1-111-1-1−ii-11-1-111ii−i−i−i−iii-1-111i−i−ii−iii−i-11
χ201-1111-1-1-1-1-1-11111-111-1-1-1ii−i−i−i−iii1-1-1-1-11111-1-111i−i1-1-1-111−ii-11-1-111−i−iiiii−i−i11-1-1i−ii−i−ii−ii1-1
χ211-1111-1-1-1-1-1-11111-111-1-1-1−i−iiiii−i−i11111-1-1-1-1-1-111−ii1-111-1-1i−i-11-1-111−i−iiiii−i−i-1-111−iii−ii−i−ii-11
χ221-1111-1-1-1-1-1-11111-111-1-1-1−i−iiiii−i−i1-1-1-1-11111-1-111−ii1-1-1-111i−i-11-1-111ii−i−i−i−iii11-1-1−ii−iii−ii−i1-1
χ231-1111-1-1-1-1-1-11111-111-1-1-1−i−iii−i−iii11111-1-1-1-111-1-1−ii1-111-1-1−ii1-111-1-1−i−iii−i−iii11-1-1−ii−ii−ii−ii1-1
χ241-1111-1-1-1-1-1-11111-111-1-1-1−i−iii−i−iii1-1-1-1-1111111-1-1−ii1-1-1-111−ii1-111-1-1ii−i−iii−i−i-1-111−iii−i−iii−i-11
χ251-1111-1-1-1-1-1-11111-1-1-111-1ii−i−iii−i−i11111-1-1-1-111-1-1i−i-11-1-111i−i1-1-1-111ii−i−iii−i−i11-1-1−ii−ii−ii−ii-11
χ261-1111-1-1-1-1-1-11111-1-1-111-1ii−i−iii−i−i1-1-1-1-1111111-1-1i−i-1111-1-1i−i1-1-1-111−i−iii−i−iii-1-111−iii−i−iii−i1-1
χ271-1111-1-1-1-1-1-11111-1-1-111-1ii−i−i−i−iii11111-1-1-1-1-1-111i−i-11-1-111−ii-1111-1-1ii−i−i−i−iii-1-111−iii−ii−i−ii1-1
χ281-1111-1-1-1-1-1-11111-1-1-111-1ii−i−i−i−iii1-1-1-1-11111-1-111i−i-1111-1-1−ii-1111-1-1−i−iiiii−i−i11-1-1−ii−iii−ii−i-11
χ291-1111-1-1-1-1-1-11111-1-1-111-1−i−iiiii−i−i11111-1-1-1-1-1-111−ii-11-1-111i−i-1111-1-1−i−iiiii−i−i-1-111i−i−ii−iii−i1-1
χ301-1111-1-1-1-1-1-11111-1-1-111-1−i−iiiii−i−i1-1-1-1-11111-1-111−ii-1111-1-1i−i-1111-1-1ii−i−i−i−iii11-1-1i−ii−i−ii−ii-11
χ311-1111-1-1-1-1-1-11111-1-1-111-1−i−iii−i−iii11111-1-1-1-111-1-1−ii-11-1-111−ii1-1-1-111−i−iii−i−iii11-1-1i−ii−ii−ii−i-11
χ321-1111-1-1-1-1-1-11111-1-1-111-1−i−iii−i−iii1-1-1-1-1111111-1-1−ii-1111-1-1−ii1-1-1-111ii−i−iii−i−i-1-111i−i−iii−i−ii1-1
χ332222222222-2-2-222-20000-222222222-2000000002222-2-2000000-2-2-2-200000000000000000000000000
χ342222222222-2-2-222-20000-22222-2-2-2-2-200000000-2-2-2-2-2-2000000222200000000000000000000000000
χ352222222222-2-2-222-20000-2-2-2-2-22222-200000000-2-2-2-222000000-2-22200000000000000000000000000
χ362222222222-2-2-222-20000-2-2-2-2-2-2-2-2-2-20000000022222200000022-2-200000000000000000000000000
χ3722222222-2-2222-2-222222-200000000-222-2-222-2-2000000-2-22-22-2000000000000000000000000000000
χ3822222222-2-2222-2-222222-200000000-2-2-222-2-222000000-2-2-22-22000000000000000000000000000000
χ3922222222-2-2222-2-22-2-2-2-2-200000000-222-2-222-2-200000022-22-22000000000000000000000000000000
χ4022222222-2-2222-2-22-2-2-2-2-200000000-2-2-222-2-222000000222-22-2000000000000000000000000000000
χ41222-2-2-2-222-20002-20000002i−2i2i−2i2-22-20i2−i2i2−i2i2−i2i2−i22i−2i2i−2i00000000000000002−22−2i2−i2i2−i22−22−20000000000
χ42222-2-2-2-222-20002-20000002i−2i2i−2i2-22-20−i2i2−i2i2−i2i2−i2i22i−2i2i−2i0000000000000000−22−22−i2i2−i2i2−22−220000000000
χ43222-2-2-2-222-20002-20000002i−2i2i−2i-22-220i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i00000000000000002−22−2−i2i2−i2i2−22−220000000000
χ44222-2-2-2-222-20002-20000002i−2i2i−2i-22-220−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i0000000000000000−22−22i2−i2i2−i22−22−20000000000
χ45222-2-2-2-222-20002-2000000−2i2i−2i2i2-22-20i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i0000000000000000−22−22i2−i2i2−i2−22−220000000000
χ46222-2-2-2-222-20002-2000000−2i2i−2i2i2-22-20−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i00000000000000002−22−2−i2i2−i2i22−22−20000000000
χ47222-2-2-2-222-20002-2000000−2i2i−2i2i-22-220i2−i2i2−i2i2−i2i2−i22i−2i2i−2i0000000000000000−22−22−i2i2−i2i22−22−20000000000
χ48222-2-2-2-222-20002-2000000−2i2i−2i2i-22-220−i2i2−i2i2−i2i2−i2i22i−2i2i−2i00000000000000002−22−2i2−i2i2−i2−22−220000000000
χ492-2222-2-2-222-222-2-2-222-2-2200000000-222-2-2-2-222000000-222-2-22000000000000000000000000000000
χ502-2222-2-2-222-222-2-2-222-2-2200000000-2-2-22222-2-2000000-22-222-2000000000000000000000000000000
χ512-2222-2-2-222-222-2-2-2-2-222200000000-222-2-2-2-2220000002-2-222-2000000000000000000000000000000
χ522-2222-2-2-222-222-2-2-2-2-222200000000-2-2-22222-2-20000002-22-2-22000000000000000000000000000000
χ532-2222-2-2-2-2-22-2-2222000022i2i−2i−2i2i2i−2i−2i-20000000022-2-2−2i2i000000−2i2i-2200000000000000000000000000
χ542-2222-2-2-2-2-22-2-2222000022i2i−2i−2i−2i−2i2i2i-200000000-2-222−2i2i0000002i−2i2-200000000000000000000000000
χ552-2222-2-2-2-2-22-2-222200002−2i−2i2i2i2i2i−2i−2i-200000000-2-2222i−2i000000−2i2i2-200000000000000000000000000
χ562-2222-2-2-2-2-22-2-222200002−2i−2i2i2i−2i−2i2i2i-20000000022-2-22i−2i0000002i−2i-2200000000000000000000000000
χ572-22-2-222-2-220002-20000002-2-222i−2i−2i2i0i2−i2i2−i2−i2i2−i2i2−2i2i2i−2i0000000000000000−i2i2i2−i2−222−2−222−20000000000
χ582-22-2-222-2-220002-20000002-2-222i−2i−2i2i0−i2i2−i2i2i2−i2i2−i2−2i2i2i−2i0000000000000000i2−i2−i2i22−2−222−2−220000000000
χ592-22-2-222-2-220002-20000002-2-22−2i2i2i−2i0i2−i2i2−i2−i2i2−i2i22i−2i−2i2i0000000000000000−i2i2i2−i22−2−222−2−220000000000
χ602-22-2-222-2-220002-20000002-2-22−2i2i2i−2i0−i2i2−i2i2i2−i2i2−i22i−2i−2i2i0000000000000000i2−i2−i2i2−222−2−222−20000000000
χ612-22-2-222-2-220002-2000000-222-22i−2i−2i2i0i2−i2i2−i2−i2i2−i2i22i−2i−2i2i0000000000000000i2−i2−i2i2−222−22−2−220000000000
χ622-22-2-222-2-220002-2000000-222-22i−2i−2i2i0−i2i2−i2i2i2−i2i2−i22i−2i−2i2i0000000000000000−i2i2i2−i22−2−22−222−20000000000
χ632-22-2-222-2-220002-2000000-222-2−2i2i2i−2i0i2−i2i2−i2−i2i2−i2i2−2i2i2i−2i0000000000000000i2−i2−i2i22−2−22−222−20000000000
χ642-22-2-222-2-220002-2000000-222-2−2i2i2i−2i0−i2i2−i2i2i2−i2i2−i2−2i2i2i−2i0000000000000000−i2i2i2−i2−222−22−2−220000000000
χ6544444444-4-4-4-4-4-4-4-40000400000000400000000000000000000000000000000000000000000000000
χ66444-4-4-4-44-44000-440000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ67444-4-4-4-44-44000-44000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ6844-44-44-4-40044-400-44-44-4000000000000000000000000000000000000000000000000000000000000
χ6944-44-44-4-40044-400-4-44-44000000000000000000000000000000000000000000000000000000000000
χ7044-44-44-4-400-4-44004000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ7144-44-44-4-400-4-4400400000000000000000000000000000000000000−2i22i2−2i22i20000000000000000000000
χ724-4444-4-4-4444-4-4-4-440000-400000000400000000000000000000000000000000000000000000000000
χ734-44-4-444-44-4000-440000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ744-44-4-444-44-4000-44000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ754-4-44-4-444004-4400-4000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ764-4-44-4-444004-4400-400000000000000000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ774-4-44-4-44400-44-40044-4-44000000000000000000000000000000000000000000000000000000000000
χ784-4-44-4-44400-44-4004-444-4000000000000000000000000000000000000000000000000000000000000
χ7988-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000000

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