Finite Group Databasebeta

← Group #225607

Character table — Group #225607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888444444444444444444888888888888888844444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ171-1-1111-1-1-1-1-1111-111111-1-1-1-11111-1-1-1-1-111-1-111-1-1ii−i−iii−i−i111-1-111-1-11111-1-1-1-11-11-1i−ii−iii−i−iii−i−i11-1-111-1-1i−ii−ii−ii−i
χ181-1-1111-1-1-1-1-1111-111111-1-1-1-11111-1-1-1-1-111-1-111-1-1−i−iii−i−iii111-1-111-1-11111-1-1-1-11-11-1−ii−ii−i−iii−i−iii11-1-111-1-1−ii−ii−ii−ii
χ191-1-1111-1-1-1-1-1111-111111-1-1-1-11111-1-1-1-1-1-1-111-1-111ii−i−iii−i−i111-1-111-1-11111-1-1-1-1-11-11i−ii−iii−i−iii−i−i-1-111-1-111−ii−ii−ii−ii
χ201-1-1111-1-1-1-1-1111-111111-1-1-1-11111-1-1-1-1-1-1-111-1-111−i−iii−i−iii111-1-111-1-11111-1-1-1-1-11-11−ii−ii−i−iii−i−iii-1-111-1-111i−ii−ii−ii−i
χ211-1-1111-1-1-1-1-1111-111111-1-1-1-1-1-1-1-11111-111-1-111-1-1ii−i−i−i−iii111-1-1-1-111-1-1-1-111111-11-1i−i−iiii−i−i−i−iii-1-111-1-111i−ii−i−ii−ii
χ221-1-1111-1-1-1-1-1111-111111-1-1-1-1-1-1-1-11111-111-1-111-1-1−i−iiiii−i−i111-1-1-1-111-1-1-1-111111-11-1−iii−i−i−iiiii−i−i-1-111-1-111−ii−iii−ii−i
χ231-1-1111-1-1-1-1-1111-111111-1-1-1-1-1-1-1-11111-1-1-111-1-111ii−i−i−i−iii111-1-1-1-111-1-1-1-11111-11-11i−i−iiii−i−i−i−iii11-1-111-1-1−ii−iii−ii−i
χ241-1-1111-1-1-1-1-1111-111111-1-1-1-1-1-1-1-11111-1-1-111-1-111−i−iiiii−i−i111-1-1-1-111-1-1-1-11111-11-11−iii−i−i−iiiii−i−i11-1-111-1-1i−ii−i−ii−ii
χ251-1-1111-1-1-1-1-1111-11-1-1-1-111111111-1-1-1-1-111-1-1-1-111ii−i−iii−i−i1-1-11111-1-1-1-1-1-111111-1-11i−ii−i−i−iii−i−iii11-1-1-1-111i−i−iii−i−ii
χ261-1-1111-1-1-1-1-1111-11-1-1-1-111111111-1-1-1-1-111-1-1-1-111−i−iii−i−iii1-1-11111-1-1-1-1-1-111111-1-11−ii−iiii−i−iii−i−i11-1-1-1-111−iii−i−iii−i
χ271-1-1111-1-1-1-1-1111-11-1-1-1-111111111-1-1-1-1-1-1-11111-1-1ii−i−iii−i−i1-1-11111-1-1-1-1-1-11111-111-1i−ii−i−i−iii−i−iii-1-11111-1-1−iii−i−iii−i
χ281-1-1111-1-1-1-1-1111-11-1-1-1-111111111-1-1-1-1-1-1-11111-1-1−i−iii−i−iii1-1-11111-1-1-1-1-1-11111-111-1−ii−iiii−i−iii−i−i-1-11111-1-1i−i−iii−i−ii
χ291-1-1111-1-1-1-1-1111-11-1-1-1-11111-1-1-1-11111-111-1-1-1-111ii−i−i−i−iii1-1-111-1-1111111-1-1-1-11-1-11i−i−ii−i−iiiii−i−i-1-11111-1-1i−i−ii−iii−i
χ301-1-1111-1-1-1-1-1111-11-1-1-1-11111-1-1-1-11111-111-1-1-1-111−i−iiiii−i−i1-1-111-1-1111111-1-1-1-11-1-11−iii−iii−i−i−i−iii-1-11111-1-1−iii−ii−i−ii
χ311-1-1111-1-1-1-1-1111-11-1-1-1-11111-1-1-1-11111-1-1-11111-1-1ii−i−i−i−iii1-1-111-1-1111111-1-1-1-1-111-1i−i−ii−i−iiiii−i−i11-1-1-1-111−iii−ii−i−ii
χ321-1-1111-1-1-1-1-1111-11-1-1-1-11111-1-1-1-11111-1-1-11111-1-1−i−iiiii−i−i1-1-111-1-1111111-1-1-1-1-111-1−iii−iii−i−i−i−iii11-1-1-1-111i−i−ii−iii−i
χ332222222222-22-2-2-220000000022222222-20000000022222222-20000-2-2-2-2000000000000-2-2-2-2000000000000000000000000
χ342222222222-22-2-2-220000000022222222-200000000-2-2-2-2-2-2-2-2-20000-2-2-2-20000000000002222000000000000000000000000
χ352222222222-22-2-2-2200000000-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2-200002222000000000000-2-222000000000000000000000000
χ362222222222-22-2-2-2200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-22222-20000222200000000000022-2-2000000000000000000000000
χ3722222222-2-22-2222-22222222200000000-22222222200000000-2-2-2-2-2000000000000-2-2-2-20000000000000000000000000000
χ3822222222-2-22-2222-22222222200000000-2-2-2-2-2-2-2-2-200000000-2-2-2-2-200000000000022220000000000000000000000000000
χ3922222222-2-22-2222-2-2-2-2-2-2-2-2-200000000-22222-2-2-2-200000000-22222000000000000-2-2220000000000000000000000000000
χ4022222222-2-22-2222-2-2-2-2-2-2-2-2-200000000-2-2-2-2-2222200000000-2222200000000000022-2-20000000000000000000000000000
χ41222-22-2-2-200202-2-2022-2-222-2-222−2−222−2−202-22-22-22-200000000000002−22−222−2−222−2−200000000000000002−22−22−22−200000000
χ42222-22-2-2-200202-2-2022-2-222-2-222−2−222−2−20-22-22-22-2200000000000002−22−222−2−222−2−20000000000000000−22−22−22−2200000000
χ43222-22-2-2-200202-2-2022-2-222-2-2−2−222−2−22202-22-22-22-20000000000000−22−22−2−222−2−2220000000000000000−22−22−22−2200000000
χ44222-22-2-2-200202-2-2022-2-222-2-2−2−222−2−2220-22-22-22-220000000000000−22−22−2−222−2−22200000000000000002−22−22−22−200000000
χ45222-22-2-2-200202-2-20-2-222-2-22222−2−222−2−202-22-2-22-2200000000000002−22−2−2−222−2−22200000000000000002−22−2−22−2200000000
χ46222-22-2-2-200202-2-20-2-222-2-22222−2−222−2−20-22-222-22-200000000000002−22−2−2−222−2−2220000000000000000−22−222−22−200000000
χ47222-22-2-2-200202-2-20-2-222-2-222−2−222−2−22202-22-2-22-220000000000000−22−2222−2−222−2−20000000000000000−22−222−22−200000000
χ48222-22-2-2-200202-2-20-2-222-2-222−2−222−2−2220-22-222-22-20000000000000−22−2222−2−222−2−200000000000000002−22−2−22−2200000000
χ4922-22-2-22-22-20-200022−22−22−22−22i−2i2i−2i2i−2i2i−2i0000000002-22-22i−2i2i−2i02−22−20000i2−i2i2−i2i2−i2i2−i2000000002−22−2i2−i2i2−i20000000000000000
χ5022-22-2-22-22-20-200022−22−22−22−22i−2i2i−2i2i−2i2i−2i000000000-22-22−2i2i−2i2i02−22−20000i2−i2i2−i2i2−i2i2−i200000000−22−22−i2i2−i2i20000000000000000
χ5122-22-2-22-22-20-200022−22−22−22−2−2i2i−2i2i−2i2i−2i2i0000000002-22-2−2i2i−2i2i02−22−20000−i2i2−i2i2−i2i2−i2i2000000002−22−2−i2i2−i2i20000000000000000
χ5222-22-2-22-22-20-200022−22−22−22−2−2i2i−2i2i−2i2i−2i2i000000000-22-222i−2i2i−2i02−22−20000−i2i2−i2i2−i2i2−i2i200000000−22−22i2−i2i2−i20000000000000000
χ5322-22-2-22-22-20-20002−22−22−22−222i−2i2i−2i2i−2i2i−2i0000000002-22-22i−2i2i−2i0−22−220000−i2i2−i2i2−i2i2−i2i200000000−22−22−i2i2−i2i20000000000000000
χ5422-22-2-22-22-20-20002−22−22−22−222i−2i2i−2i2i−2i2i−2i000000000-22-22−2i2i−2i2i0−22−220000−i2i2−i2i2−i2i2−i2i2000000002−22−2i2−i2i2−i20000000000000000
χ5522-22-2-22-22-20-20002−22−22−22−22−2i2i−2i2i−2i2i−2i2i0000000002-22-2−2i2i−2i2i0−22−220000i2−i2i2−i2i2−i2i2−i200000000−22−22i2−i2i2−i20000000000000000
χ5622-22-2-22-22-20-20002−22−22−22−22−2i2i−2i2i−2i2i−2i2i000000000-22-222i−2i2i−2i0−22−220000i2−i2i2−i2i2−i2i2−i2000000002−22−2−i2i2−i2i20000000000000000
χ572-222-2-2-22-220-200022−22−2−22−222i−2i2i−2i−2i2i−2i2i0000000002i−2i−2i2i-222-202−2−220000i2−i2i2−i2−i2i2−i2i200000000i2−i2−i2i2−222−20000000000000000
χ582-222-2-2-22-220-200022−22−2−22−222i−2i2i−2i−2i2i−2i2i000000000−2i2i2i−2i2-2-2202−2−220000i2−i2i2−i2−i2i2−i2i200000000−i2i2i2−i22−2−220000000000000000
χ592-222-2-2-22-220-200022−22−2−22−22−2i2i−2i2i2i−2i2i−2i0000000002i−2i−2i2i2-2-2202−2−220000−i2i2−i2i2i2−i2i2−i200000000i2−i2−i2i22−2−220000000000000000
χ602-222-2-2-22-220-200022−22−2−22−22−2i2i−2i2i2i−2i2i−2i000000000−2i2i2i−2i-222-202−2−220000−i2i2−i2i2i2−i2i2−i200000000−i2i2i2−i2−222−20000000000000000
χ612-222-2-2-22-220-20002−22−222−22−22i−2i2i−2i−2i2i−2i2i0000000002i−2i−2i2i-222-20−222−20000−i2i2−i2i2i2−i2i2−i200000000−i2i2i2−i22−2−220000000000000000
χ622-222-2-2-22-220-20002−22−222−22−22i−2i2i−2i−2i2i−2i2i000000000−2i2i2i−2i2-2-220−222−20000−i2i2−i2i2i2−i2i2−i200000000i2−i2−i2i2−222−20000000000000000
χ632-222-2-2-22-220-20002−22−222−22−2−2i2i−2i2i2i−2i2i−2i0000000002i−2i−2i2i2-2-220−222−20000i2−i2i2−i2−i2i2−i2i200000000−i2i2i2−i2−222−20000000000000000
χ642-222-2-2-22-220-20002−22−222−22−2−2i2i−2i2i2i−2i2i−2i000000000−2i2i2i−2i-222-20−222−20000i2−i2i2−i2−i2i2−i2i200000000i2−i2−i2i22−2−220000000000000000
χ652-2-2222-2-222-2-222-2-22222-2-2-2-200000000222-2-222-2-200000000-2-2-222000000000000-22-220000000000000000000000000000
χ662-2-2222-2-222-2-222-2-22222-2-2-2-2000000002-2-222-2-22200000000-2-2-2220000000000002-22-20000000000000000000000000000
χ672-2-2222-2-222-2-222-2-2-2-2-2-2222200000000222-2-2-2-22200000000-222-2-2000000000000-222-20000000000000000000000000000
χ682-2-2222-2-222-2-222-2-2-2-2-2-22222000000002-2-22222-2-200000000-222-2-20000000000002-2-220000000000000000000000000000
χ692-2-2222-2-2-2-222-2-222000000002222-2-2-2-22000000002i2i−2i−2i2i2i−2i−2i-20000-2-222000000000000−2i2i−2i2i000000000000000000000000
χ702-2-2222-2-2-2-222-2-222000000002222-2-2-2-2200000000−2i−2i2i2i−2i−2i2i2i-20000-2-2220000000000002i−2i2i−2i000000000000000000000000
χ712-2-2222-2-2-2-222-2-22200000000-2-2-2-222222000000002i2i−2i−2i−2i−2i2i2i-2000022-2-2000000000000−2i2i2i−2i000000000000000000000000
χ722-2-2222-2-2-2-222-2-22200000000-2-2-2-22222200000000−2i−2i2i2i2i2i−2i−2i-2000022-2-20000000000002i−2i−2i2i000000000000000000000000
χ732-2-2-22-22200-202-22022-2-2-2-22222−2−2−2−22202-2-222-2-2200000000000002−2−2222−2−2−2−22200000000000000002−2−222−2−2200000000
χ742-2-2-22-22200-202-22022-2-2-2-22222−2−2−2−2220-222-2-222-200000000000002−2−2222−2−2−2−2220000000000000000−222−2−222−200000000
χ752-2-2-22-22200-202-22022-2-2-2-222−2−22222−2−202-2-222-2-220000000000000−222−2−2−22222−2−20000000000000000−222−2−222−200000000
χ762-2-2-22-22200-202-22022-2-2-2-222−2−22222−2−20-222-2-222-20000000000000−222−2−2−22222−2−200000000000000002−2−222−2−2200000000
χ772-2-2-22-22200-202-220-2-22222-2-222−2−2−2−22202-2-22-222-200000000000002−2−22−2−22222−2−200000000000000002−2−22−222−200000000
χ782-2-2-22-22200-202-220-2-22222-2-222−2−2−2−2220-222-22-2-2200000000000002−2−22−2−22222−2−20000000000000000−222−22−2−2200000000
χ792-2-2-22-22200-202-220-2-22222-2-2−2−22222−2−202-2-22-222-20000000000000−222−222−2−2−2−2220000000000000000−222−22−2−2200000000
χ802-2-2-22-22200-202-220-2-22222-2-2−2−22222−2−20-222-22-2-220000000000000−222−222−2−2−2−22200000000000000002−2−22−222−200000000
χ8144444444-4-4-4-4-4-4-4-40000000000000000400000000000000004000000000000000000000000000000000000000000000000
χ82444-44-4-4-400-40-4440000000002222−22−222222−22−220000000000000000000000−2222−22220000000000000000000000000000000000000000
χ83444-44-4-4-400-40-444000000000−22−222222−22−222222000000000000000000000022−2222−220000000000000000000000000000000000000000
χ8444-44-4-44-4-4404000-422−2222−2222−2222−2200000000000000000000000000−2222−222200000000000000000000000000000000000000000000
χ8544-44-4-44-4-4404000-4−2222−2222−2222−22220000000000000000000000000022−2222−2200000000000000000000000000000000000000000000
χ8644-4-4-44-440000000022−22−222222−22−22222i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ8744-4-4-44-440000000022−22−222222−22−2222−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ8844-4-4-44-4400000000−222222−22−222222−222i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ8944-4-4-44-4400000000−222222−22−222222−22−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ904-444-4-4-444-404000-422−2222−22−2222−222200000000000000000000000000−222222−2200000000000000000000000000000000000000000000
χ914-444-4-4-444-404000-4−2222−222222−2222−220000000000000000000000000022−22−222200000000000000000000000000000000000000000000
χ924-44-4-444-40000000022−22−2222−222222−222i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ934-44-4-444-40000000022−22−2222−222222−22−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ944-44-4-444-400000000−222222−2222−22−22222i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ954-44-4-444-400000000−222222−2222−22−2222−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ964-4-4444-4-4444-4-4-44-40000000000000000-400000000000000004000000000000000000000000000000000000000000000000
χ974-4-4-44-4440040-44-40000000002222−22−22−22−2222220000000000000000000000−222222−220000000000000000000000000000000000000000
χ984-4-4-44-4440040-44-4000000000−22−2222222222−22−22000000000000000000000022−22−22220000000000000000000000000000000000000000

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