Finite Group Databasebeta

← Group #229283

Character table — Group #229283

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111122222222222222222222222244444444444444444444444444444444448888888888888888888888881616161616161616
order12222222444444448888888888888888222244444444444444888888888888888844444444888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111-1-1-1-1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-11111-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ101111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-11111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ171-11-111-1-1-111-1-1-111iiii−i−i−i−i1111-1-1-1-111-1-11ii−i−iii−i−iii−i−i-1ii−i−i11-1-1iiii−i−i−i−ii−i1-1i−ii−iii−i−i11-1-111-1-111-1-11-11-1i−ii−i
χ181-11-111-1-1-111-1-1-111iiii−i−i−i−i1111-1-1-1-111-1-11−i−iiiii−i−i−i−iii-1ii−i−i11-1-1iiii−i−i−i−ii−i1-1−ii−iiii−i−i11-1-1-1-111-1-111-11-11−ii−ii
χ191-11-111-1-1-111-1-1-111iiii−i−i−i−i1111-1-1-1-1-1-1111ii−i−i−i−iiiii−i−i-1ii−i−i11-1-1iiii−i−i−i−i−ii-11i−ii−i−i−iii-1-11111-1-111-1-1-11-11−ii−ii
χ201-11-111-1-1-111-1-1-111iiii−i−i−i−i1111-1-1-1-1-1-1111−i−iii−i−iii−i−iii-1ii−i−i11-1-1iiii−i−i−i−i−ii-11−ii−ii−i−iii-1-111-1-111-1-1111-11-1i−ii−i
χ211-11-111-1-1-111-1-1-111iiii−i−i−i−i-1-1-1-1111111-1-11ii−i−iii−i−i−i−iii-1ii−i−i-1-111−i−i−i−iiiiii−i1-1−iii−i−i−iii-1-11111-1-1-1-111-111-1i−i−ii
χ221-11-111-1-1-111-1-1-111iiii−i−i−i−i-1-1-1-1111111-1-11−i−iiiii−i−iii−i−i-1ii−i−i-1-111−i−i−i−iiiiii−i1-1i−i−ii−i−iii-1-111-1-11111-1-11-1-11−iii−i
χ231-11-111-1-1-111-1-1-111iiii−i−i−i−i-1-1-1-11111-1-1111ii−i−i−i−iii−i−iii-1ii−i−i-1-111−i−i−i−iiiii−ii-11−iii−iii−i−i11-1-111-1-1-1-1111-1-11−iii−i
χ241-11-111-1-1-111-1-1-111iiii−i−i−i−i-1-1-1-11111-1-1111−i−iii−i−iiiii−i−i-1ii−i−i-1-111−i−i−i−iiiii−ii-11i−i−iiii−i−i11-1-1-1-11111-1-1-111-1i−i−ii
χ251-11-111-1-1-111-1-1-111−i−i−i−iiiii1111-1-1-1-111-1-11ii−i−i−i−iiiii−i−i-1−i−iii11-1-1−i−i−i−iiiii−ii1-1i−ii−i−i−iii11-1-1-1-111-1-111-11-11i−ii−i
χ261-11-111-1-1-111-1-1-111−i−i−i−iiiii1111-1-1-1-111-1-11−i−iii−i−iii−i−iii-1−i−iii11-1-1−i−i−i−iiiii−ii1-1−ii−ii−i−iii11-1-111-1-111-1-11-11-1−ii−ii
χ271-11-111-1-1-111-1-1-111−i−i−i−iiiii1111-1-1-1-1-1-1111ii−i−iii−i−iii−i−i-1−i−iii11-1-1−i−i−i−iiiiii−i-11i−ii−iii−i−i-1-111-1-111-1-1111-11-1−ii−ii
χ281-11-111-1-1-111-1-1-111−i−i−i−iiiii1111-1-1-1-1-1-1111−i−iiiii−i−i−i−iii-1−i−iii11-1-1−i−i−i−iiiiii−i-11−ii−iiii−i−i-1-11111-1-111-1-1-11-11i−ii−i
χ291-11-111-1-1-111-1-1-111−i−i−i−iiiii-1-1-1-1111111-1-11ii−i−i−i−iii−i−iii-1−i−iii-1-111iiii−i−i−i−i−ii1-1−iii−iii−i−i-1-111-1-11111-1-11-1-11i−i−ii
χ301-11-111-1-1-111-1-1-111−i−i−i−iiiii-1-1-1-1111111-1-11−i−iii−i−iiiii−i−i-1−i−iii-1-111iiii−i−i−i−i−ii1-1i−i−iiii−i−i-1-11111-1-1-1-111-111-1−iii−i
χ311-11-111-1-1-111-1-1-111−i−i−i−iiiii-1-1-1-11111-1-1111ii−i−iii−i−i−i−iii-1−i−iii-1-111iiii−i−i−i−ii−i-11−iii−i−i−iii11-1-1-1-11111-1-1-111-1−iii−i
χ321-11-111-1-1-111-1-1-111−i−i−i−iiiii-1-1-1-11111-1-1111−i−iiiii−i−iii−i−i-1−i−iii-1-111iiii−i−i−i−ii−i-11i−i−ii−i−iii11-1-111-1-1-1-1111-1-11i−i−ii
χ33222222222-22-2-222-200000000222222220000-2222200002222-20000-2-2-2-2000000000000-2-2-2-2000000000000000000000000
χ34222222222-22-2-222-200000000222222220000-2-2-2-2-20000-2-2-2-2-20000-2-2-2-20000000000002222000000000000000000000000
χ35222222222-22-2-222-200000000-2-2-2-2-2-2-2-20000-222220000-2-2-2-2-20000222200000000000022-2-2000000000000000000000000
χ36222222222-22-2-222-200000000-2-2-2-2-2-2-2-20000-2-2-2-2-200002222-200002222000000000000-2-222000000000000000000000000
χ3722222222-22-222-2-2222222222000000002222-2000022220000-2-2-2-2-2000000000000-2-2-2-20000000000000000000000000000
χ3822222222-22-222-2-222222222200000000-2-2-2-2-20000-2-2-2-20000-2-2-2-2-200000000000022220000000000000000000000000000
χ3922222222-22-222-2-22-2-2-2-2-2-2-2-2000000002222-20000-2-2-2-20000-2222200000000000022-2-20000000000000000000000000000
χ4022222222-22-222-2-22-2-2-2-2-2-2-2-200000000-2-2-2-2-2000022220000-22222000000000000-2-2220000000000000000000000000000
χ4122-22-22-2-20-202-20022i2i−2i−2i2i2i−2i−2i22−2−222−2−22-22-2000002i−2i2i−2i0000000002−22−2i2i2−i2−i2i2i2−i2−i200000000i2−i2i2−i22−22−20000000000000000
χ4222-22-22-2-20-202-20022i2i−2i−2i2i2i−2i−2i22−2−222−2−2-22-2200000−2i2i−2i2i0000000002−22−2i2i2−i2−i2i2i2−i2−i200000000−i2i2−i2i2−22−220000000000000000
χ4322-22-22-2-20-202-20022i2i−2i−2i2i2i−2i−2i−2−222−2−2222-22-2000002i−2i2i−2i000000000−22−22−i2−i2i2i2−i2−i2i2i200000000−i2i2−i2i2−22−220000000000000000
χ4422-22-22-2-20-202-20022i2i−2i−2i2i2i−2i−2i−2−222−2−222-22-2200000−2i2i−2i2i000000000−22−22−i2−i2i2i2−i2−i2i2i200000000i2−i2i2−i22−22−20000000000000000
χ4522-22-22-2-20-202-2002−2i−2i2i2i−2i−2i2i2i22−2−222−2−22-22-200000−2i2i−2i2i0000000002−22−2−i2−i2i2i2−i2−i2i2i200000000−i2i2−i2i22−22−20000000000000000
χ4622-22-22-2-20-202-2002−2i−2i2i2i−2i−2i2i2i22−2−222−2−2-22-22000002i−2i2i−2i0000000002−22−2−i2−i2i2i2−i2−i2i2i200000000i2−i2i2−i2−22−220000000000000000
χ4722-22-22-2-20-202-2002−2i−2i2i2i−2i−2i2i2i−2−222−2−2222-22-200000−2i2i−2i2i000000000−22−22i2i2−i2−i2i2i2−i2−i200000000i2−i2i2−i2−22−220000000000000000
χ4822-22-22-2-20-202-2002−2i−2i2i2i−2i−2i2i2i−2−222−2−222-22-22000002i−2i2i−2i000000000−22−22i2i2−i2−i2i2i2−i2−i200000000−i2i2−i2i22−22−20000000000000000
χ4922-2-22-22-2-202002-20i2−i2i2−i2i2−i2i2−i22i−2i2i−2i2i−2i2i−2i000002-22-200002i−2i2i−2i0i2−i2i2−i200002−22−22−22−20000000000000000i2−i2i2−i22−22−200000000
χ5022-2-22-22-2-202002-20i2−i2i2−i2i2−i2i2−i22i−2i2i−2i2i−2i2i−2i00000-22-220000−2i2i−2i2i0i2−i2i2−i200002−22−22−22−20000000000000000−i2i2−i2i2−22−2200000000
χ5122-2-22-22-2-202002-20i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i−2i2i−2i2i000002-22-20000−2i2i−2i2i0i2−i2i2−i20000−22−22−22−220000000000000000i2−i2i2−i2−22−2200000000
χ5222-2-22-22-2-202002-20i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i−2i2i−2i2i00000-22-2200002i−2i2i−2i0i2−i2i2−i20000−22−22−22−220000000000000000−i2i2−i2i22−22−200000000
χ5322-2-22-22-2-202002-20−i2i2−i2i2−i2i2−i2i22i−2i2i−2i2i−2i2i−2i000002-22-200002i−2i2i−2i0−i2i2−i2i20000−22−22−22−220000000000000000−i2i2−i2i2−22−2200000000
χ5422-2-22-22-2-202002-20−i2i2−i2i2−i2i2−i2i22i−2i2i−2i2i−2i2i−2i00000-22-220000−2i2i−2i2i0−i2i2−i2i20000−22−22−22−220000000000000000i2−i2i2−i22−22−200000000
χ5522-2-22-22-2-202002-20−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i−2i2i−2i2i000002-22-20000−2i2i−2i2i0−i2i2−i2i200002−22−22−22−20000000000000000−i2i2−i2i22−22−200000000
χ5622-2-22-22-2-202002-20−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i−2i2i−2i2i00000-22-2200002i−2i2i−2i0−i2i2−i2i200002−22−22−22−20000000000000000i2−i2i2−i2−22−2200000000
χ572-22-222-2-222-2-2-22-222i2i2i2i−2i−2i−2i−2i0000000022-2-2-200002i2i−2i−2i00002−2i−2i2i2i000000000000−2i2i-220000000000000000000000000000
χ582-22-222-2-222-2-2-22-222i2i2i2i−2i−2i−2i−2i00000000-2-222-20000−2i−2i2i2i00002−2i−2i2i2i0000000000002i−2i2-20000000000000000000000000000
χ592-22-222-2-222-2-2-22-22−2i−2i−2i−2i2i2i2i2i0000000022-2-2-20000−2i−2i2i2i000022i2i−2i−2i0000000000002i−2i-220000000000000000000000000000
χ602-22-222-2-222-2-2-22-22−2i−2i−2i−2i2i2i2i2i00000000-2-222-200002i2i−2i−2i000022i2i−2i−2i000000000000−2i2i2-20000000000000000000000000000
χ612-22-222-2-2-2-2222-22-2000000002222-2-2-2-20000-22i2i−2i−2i00002i2i−2i−2i20000-2-222000000000000−2i2i−2i2i000000000000000000000000
χ622-22-222-2-2-2-2222-22-2000000002222-2-2-2-20000-2−2i−2i2i2i0000−2i−2i2i2i20000-2-2220000000000002i−2i2i−2i000000000000000000000000
χ632-22-222-2-2-2-2222-22-200000000-2-2-2-222220000-22i2i−2i−2i0000−2i−2i2i2i2000022-2-20000000000002i−2i−2i2i000000000000000000000000
χ642-22-222-2-2-2-2222-22-200000000-2-2-2-222220000-2−2i−2i2i2i00002i2i−2i−2i2000022-2-2000000000000−2i2i2i−2i000000000000000000000000
χ652-2-222-2-2220200-2-202−22−2−22−222i−2i2i−2i−2i2i−2i2i000002i−2i−2i2i0000-222-202−2−220000−i2i2−i2i2i2−i2i2−i20000000000000000−i2i2i2−i2−222−200000000
χ662-2-222-2-2220200-2-202−22−2−22−222i−2i2i−2i−2i2i−2i2i00000−2i2i2i−2i00002-2-2202−2−220000−i2i2−i2i2i2−i2i2−i20000000000000000i2−i2−i2i22−2−2200000000
χ672-2-222-2-2220200-2-202−22−2−22−22−2i2i−2i2i2i−2i2i−2i000002i−2i−2i2i00002-2-2202−2−220000i2−i2i2−i2−i2i2−i2i20000000000000000−i2i2i2−i22−2−2200000000
χ682-2-222-2-2220200-2-202−22−2−22−22−2i2i−2i2i2i−2i2i−2i00000−2i2i2i−2i0000-222-202−2−220000i2−i2i2−i2−i2i2−i2i20000000000000000i2−i2−i2i2−222−200000000
χ692-2-222-2-2220200-2-20−22−222−22−22i−2i2i−2i−2i2i−2i2i000002i−2i−2i2i0000-222-20−222−20000i2−i2i2−i2−i2i2−i2i20000000000000000i2−i2−i2i22−2−2200000000
χ702-2-222-2-2220200-2-20−22−222−22−22i−2i2i−2i−2i2i−2i2i00000−2i2i2i−2i00002-2-220−222−20000i2−i2i2−i2−i2i2−i2i20000000000000000−i2i2i2−i2−222−200000000
χ712-2-222-2-2220200-2-20−22−222−22−2−2i2i−2i2i2i−2i2i−2i000002i−2i−2i2i00002-2-220−222−20000−i2i2−i2i2i2−i2i2−i20000000000000000i2−i2−i2i2−222−200000000
χ722-2-222-2-2220200-2-20−22−222−22−2−2i2i−2i2i2i−2i2i−2i00000−2i2i2i−2i0000-222-20−222−20000−i2i2−i2i2i2−i2i2−i20000000000000000−i2i2i2−i22−2−2200000000
χ732-2-2-2-22220-20-2200222-2-2-2-22222−2−2−2−2222-2-22000002-2-220000000002−2−2222−2−2−2−222000000002−2−222−2−220000000000000000
χ742-2-2-2-22220-20-2200222-2-2-2-22222−2−2−2−222-222-200000-222-20000000002−2−2222−2−2−2−22200000000−222−2−222−20000000000000000
χ752-2-2-2-22220-20-2200222-2-2-2-222−2−22222−2−22-2-22000002-2-22000000000−222−2−2−22222−2−200000000−222−2−222−20000000000000000
χ762-2-2-2-22220-20-2200222-2-2-2-222−2−22222−2−2-222-200000-222-2000000000−222−2−2−22222−2−2000000002−2−222−2−220000000000000000
χ772-2-2-2-22220-20-22002-2-22222-2-222−2−2−2−2222-2-2200000-222-20000000002−2−22−2−22222−2−200000000−222−22−2−220000000000000000
χ782-2-2-2-22220-20-22002-2-22222-2-222−2−2−2−222-222-2000002-2-220000000002−2−22−2−22222−2−2000000002−2−22−222−20000000000000000
χ792-2-2-2-22220-20-22002-2-22222-2-2−2−22222−2−22-2-2200000-222-2000000000−222−222−2−2−2−222000000002−2−22−222−20000000000000000
χ802-2-2-2-22220-20-22002-2-22222-2-2−2−22222−2−2-222-2000002-2-22000000000−222−222−2−2−2−22200000000−222−22−2−220000000000000000
χ8144444444-4-4-4-4-4-4-4-40000000000000000000040000000000004000000000000000000000000000000000000000000000000
χ82444-4-4-4-440000000022−22−222222−22−22222i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ83444-4-4-4-440000000022−22−222222−22−2222−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ84444-4-4-4-4400000000−222222−22−222222−222i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ85444-4-4-4-4400000000−222222−22−222222−22−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ8644-44-44-4-4040-4400-4000000002222−22−222222−22−220000000000000000000000−2222−22220000000000000000000000000000000000000000
χ8744-44-44-4-4040-4400-400000000−22−222222−22−222222000000000000000000000022−2222−220000000000000000000000000000000000000000
χ8844-4-44-44-440-400-4402i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ8944-4-44-44-440-400-440−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ904-444-4-44-4000000002i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000002-2-22-222-200000000000000000000000000000000
χ914-444-4-44-4000000002i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ924-444-4-44-400000000−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ934-444-4-44-400000000−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000002-2-22-222-200000000000000000000000000000000
χ944-44-444-4-44-4-4444-4-4000000000000000000004000000000000-4000000000000000000000000000000000000000000000000
χ954-4-444-4-44-40-40044022−2222−22−2222−222200000000000000000000000000−222222−2200000000000000000000000000000000000000000000
χ964-4-444-4-44-40-400440−2222−222222−2222−220000000000000000000000000022−22−222200000000000000000000000000000000000000000000
χ974-4-4-4-44440404-400-4000000002222−22−22−22−2222220000000000000000000000−222222−220000000000000000000000000000000000000000
χ984-4-4-4-44440404-400-400000000−22−2222222222−22−22000000000000000000000022−22−22220000000000000000000000000000000000000000

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