Finite Group Databasebeta

← Group #192595

Character table — Group #192595

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222244444444444444444488888888888888881616111111112222222244444444444444444488888888888888881616
order12222222444444442222444444888888884444444488888888442222222244444444222244444488888888444444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1111111111111111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-11111-1-11111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ71111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91-1-1111-1-111-11-1-1-1111-1-1-1ii−i−i11111-1-1-1-11-1i−iii−i−i11-1-1ii−i−ii−i1-1-1111-1-111-11-1-1-1111-1-1-1ii−i−i11111-1-1-1-11-1i−iii−i−i11-1-1ii−i−ii−i
χ101-1-1111-1-111-11-1-1-1111-1-1-1ii−i−i1-1-1-1-111111-1i−iii−i−i-1-111−i−iii−ii1-1-1111-1-111-11-1-1-1111-1-1-1ii−i−i1-1-1-1-111111-1i−iii−i−i-1-111−i−iii−ii
χ111-1-1111-1-111-11-1-1-1111-1-1-1−i−iii11111-1-1-1-11-1−ii−i−iii11-1-1−i−iii−ii1-1-1111-1-111-11-1-1-1111-1-1-1−i−iii11111-1-1-1-11-1−ii−i−iii11-1-1−i−iii−ii
χ121-1-1111-1-111-11-1-1-1111-1-1-1−i−iii1-1-1-1-111111-1−ii−i−iii-1-111ii−i−ii−i1-1-1111-1-111-11-1-1-1111-1-1-1−i−iii1-1-1-1-111111-1−ii−i−iii-1-111ii−i−ii−i
χ131-1-1111-1-111-11-1-1-11-1-111-1ii−i−i11111-1-1-1-1-11i−i−i−iii-1-111ii−i−i−ii1-1-1111-1-111-11-1-1-11-1-111-1ii−i−i11111-1-1-1-1-11i−i−i−iii-1-111ii−i−i−ii
χ141-1-1111-1-111-11-1-1-11-1-111-1ii−i−i1-1-1-1-11111-11i−i−i−iii11-1-1−i−iiii−i1-1-1111-1-111-11-1-1-11-1-111-1ii−i−i1-1-1-1-11111-11i−i−i−iii11-1-1−i−iiii−i
χ151-1-1111-1-111-11-1-1-11-1-111-1−i−iii11111-1-1-1-1-11−iiii−i−i-1-111−i−iiii−i1-1-1111-1-111-11-1-1-11-1-111-1−i−iii11111-1-1-1-1-11−iiii−i−i-1-111−i−iiii−i
χ161-1-1111-1-111-11-1-1-11-1-111-1−i−iii1-1-1-1-11111-11−iiii−i−i11-1-1ii−i−i−ii1-1-1111-1-111-11-1-1-11-1-111-1−i−iii1-1-1-1-11111-11−iiii−i−i11-1-1ii−i−i−ii
χ1722222222222-2-2-22-22222-20000-200000000-2-2000000000000000022222222222-2-2-22-22222-20000-200000000-2-20000000000000000
χ1822222222222-2-2-22-2-2-2-2-2-20000-20000000022000000000000000022222222222-2-2-22-2-2-2-2-2-20000-200000000220000000000000000
χ1922222222-2-2-2222-220000-22222-20000000000-2-20000000000000022222222-2-2-2222-220000-22222-20000000000-2-200000000000000
χ2022222222-2-2-2222-220000-2-2-2-2-2-20000000000220000000000000022222222-2-2-2222-220000-2-2-2-2-2-200000000002200000000000000
χ2122222222-2-2-2-2-2-2-2-200002000020000000000002-22-2000000000022222222-2-2-2-2-2-2-2-200002000020000000000002-22-20000000000
χ2222222222-2-2-2-2-2-2-2-20000200002000000000000-22-22000000000022222222-2-2-2-2-2-2-2-20000200002000000000000-22-220000000000
χ232222-2-2-2-22-22000-202-22-200000022−2−222−2−2000000002−22−20000002222-2-2-2-22-22000-202-22-200000022−2−222−2−2000000002−22−2000000
χ242222-2-2-2-22-22000-202-22-2000000−2−222−2−22200000000−22−220000002222-2-2-2-22-22000-202-22-2000000−2−222−2−22200000000−22−22000000
χ252222-2-2-2-22-22000-20-22-2200000022−2−222−2−200000000−22−220000002222-2-2-2-22-22000-20-22-2200000022−2−222−2−200000000−22−22000000
χ262222-2-2-2-22-22000-20-22-22000000−2−222−2−222000000002−22−20000002222-2-2-2-22-22000-20-22-22000000−2−222−2−222000000002−22−2000000
χ2722-2-2-222-200022-20-2000002-22-20i2−i2i2−i2i2−i2i2−i2000000000000i2−i2i2−i20022-2-2-222-200022-20-2000002-22-20i2−i2i2−i2i2−i2i2−i2000000000000i2−i2i2−i200
χ2822-2-2-222-200022-20-2000002-22-20−i2i2−i2i2−i2i2−i2i2000000000000−i2i2−i2i20022-2-2-222-200022-20-2000002-22-20−i2i2−i2i2−i2i2−i2i2000000000000−i2i2−i2i200
χ2922-2-2-222-200022-20-200000-22-220i2−i2i2−i2i2−i2i2−i2000000000000−i2i2−i2i20022-2-2-222-200022-20-200000-22-220i2−i2i2−i2i2−i2i2−i2000000000000−i2i2−i2i200
χ3022-2-2-222-200022-20-200000-22-220−i2i2−i2i2−i2i2−i2i2000000000000i2−i2i2−i20022-2-2-222-200022-20-200000-22-220−i2i2−i2i2−i2i2−i2i2000000000000i2−i2i2−i200
χ312-22-2-22-220002-220-2000002i−2i−2i2i0i2−i2i2−i2−i2i2−i2i2000000000000−222−2002-22-2-22-220002-220-2000002i−2i−2i2i0i2−i2i2−i2−i2i2−i2i2000000000000−222−200
χ322-22-2-22-220002-220-2000002i−2i−2i2i0−i2i2−i2i2i2−i2i2−i20000000000002−2−22002-22-2-22-220002-220-2000002i−2i−2i2i0−i2i2−i2i2i2−i2i2−i20000000000002−2−2200
χ332-22-2-22-220002-220-200000−2i2i2i−2i0i2−i2i2−i2−i2i2−i2i20000000000002−2−22002-22-2-22-220002-220-200000−2i2i2i−2i0i2−i2i2−i2−i2i2−i2i20000000000002−2−2200
χ342-22-2-22-220002-220-200000−2i2i2i−2i0−i2i2−i2i2i2−i2i2−i2000000000000−222−2002-22-2-22-220002-220-200000−2i2i2i−2i0−i2i2−i2i2i2−i2i2−i2000000000000−222−200
χ352-2-2222-2-222-2-222-2-222-2-220000-200000000-2200000000000000002-2-2222-2-222-2-222-2-222-2-220000-200000000-220000000000000000
χ362-2-2222-2-222-2-222-2-2-2-22220000-2000000002-200000000000000002-2-2222-2-222-2-222-2-2-2-22220000-2000000002-20000000000000000
χ372-2-2222-2-2-2-222-2-222000022i2i−2i−2i-20000000000−2i2i000000000000002-2-2222-2-2-2-222-2-222000022i2i−2i−2i-20000000000−2i2i00000000000000
χ382-2-2222-2-2-2-222-2-22200002−2i−2i2i2i-200000000002i−2i000000000000002-2-2222-2-2-2-222-2-22200002−2i−2i2i2i-200000000002i−2i00000000000000
χ392-2-2222-2-2-2-22-2222-20000-2000020000000000002i−2i−2i2i00000000002-2-2222-2-2-2-22-2222-20000-2000020000000000002i−2i−2i2i0000000000
χ402-2-2222-2-2-2-22-2222-20000-200002000000000000−2i2i2i−2i00000000002-2-2222-2-2-2-22-2222-20000-200002000000000000−2i2i2i−2i0000000000
χ412-2-22-2-2222-2-2000202-2-2200000022−2−2−2−222000000002−2−220000002-2-22-2-2222-2-2000202-2-2200000022−2−2−2−222000000002−2−22000000
χ422-2-22-2-2222-2-2000202-2-22000000−2−22222−2−200000000−222−20000002-2-22-2-2222-2-2000202-2-22000000−2−22222−2−200000000−222−2000000
χ432-2-22-2-2222-2-200020-222-200000022−2−2−2−22200000000−222−20000002-2-22-2-2222-2-200020-222-200000022−2−2−2−22200000000−222−2000000
χ442-2-22-2-2222-2-200020-222-2000000−2−22222−2−2000000002−2−220000002-2-22-2-2222-2-200020-222-2000000−2−22222−2−2000000002−2−22000000
χ454444-4-4-4-4-44-4000400000000000000000000000000000000000004444-4-4-4-4-44-400040000000000000000000000000000000000000
χ4644-4-44-4-440000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000044-4-44-4-440000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ4744-4-44-4-44000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000044-4-44-4-44000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ4844-4-4-444-4000-4-440400000000000000000000000000000000000044-4-4-444-4000-4-4404000000000000000000000000000000000000
χ494-44-44-44-40000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000004-44-44-44-40000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ504-44-44-44-4000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000004-44-44-44-4000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ514-44-4-44-44000-44-4040000000000000000000000000000000000004-44-4-44-44000-44-404000000000000000000000000000000000000
χ524-4-44-4-444-444000-400000000000000000000000000000000000004-4-44-4-444-444000-40000000000000000000000000000000000000
χ531111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ5411111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111
χ55111111111111111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111
χ56111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111111-1-11111111111-1-1-1-1-1-1
χ571111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111
χ581111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1
χ591111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ601111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ611-1-1111-1-111-11-1-1-1111-1-1-1ii−i−i11111-1-1-1-11-1i−iii−i−i11-1-1ii−i−ii−i-111-1-1-111-1-11-1111-1-1-1111−i−iii-1-1-1-1-11111-11−ii−i−iii-1-111−i−iii−ii
χ621-1-1111-1-111-11-1-1-1111-1-1-1ii−i−i1-1-1-1-111111-1i−iii−i−i-1-111−i−iii−ii-111-1-1-111-1-11-1111-1-1-1111−i−iii-11111-1-1-1-1-11−ii−i−iii11-1-1ii−i−ii−i
χ631-1-1111-1-111-11-1-1-1111-1-1-1−i−iii11111-1-1-1-11-1−ii−i−iii11-1-1−i−iii−ii-111-1-1-111-1-11-1111-1-1-1111ii−i−i-1-1-1-1-11111-11i−iii−i−i-1-111ii−i−ii−i
χ641-1-1111-1-111-11-1-1-1111-1-1-1−i−iii1-1-1-1-111111-1−ii−i−iii-1-111ii−i−ii−i-111-1-1-111-1-11-1111-1-1-1111ii−i−i-11111-1-1-1-1-11i−iii−i−i11-1-1−i−iii−ii
χ651-1-1111-1-111-11-1-1-11-1-111-1ii−i−i11111-1-1-1-1-11i−i−i−iii-1-111ii−i−i−ii-111-1-1-111-1-11-1111-111-1-11−i−iii-1-1-1-1-111111-1−iiii−i−i11-1-1−i−iiii−i
χ661-1-1111-1-111-11-1-1-11-1-111-1ii−i−i1-1-1-1-11111-11i−i−i−iii11-1-1−i−iiii−i-111-1-1-111-1-11-1111-111-1-11−i−iii-11111-1-1-1-11-1−iiii−i−i-1-111ii−i−i−ii
χ671-1-1111-1-111-11-1-1-11-1-111-1−i−iii11111-1-1-1-1-11−iiii−i−i-1-111−i−iiii−i-111-1-1-111-1-11-1111-111-1-11ii−i−i-1-1-1-1-111111-1i−i−i−iii11-1-1ii−i−i−ii
χ681-1-1111-1-111-11-1-1-11-1-111-1−i−iii1-1-1-1-11111-11−iiii−i−i11-1-1ii−i−i−ii-111-1-1-111-1-11-1111-111-1-11ii−i−i-11111-1-1-1-11-1i−i−i−iii-1-111−i−iiii−i
χ6922222222222-2-2-22-22222-20000-200000000-2-20000000000000000-2-2-2-2-2-2-2-2-2-2-2222-22-2-2-2-220000200000000220000000000000000
χ7022222222222-2-2-22-2-2-2-2-2-20000-200000000220000000000000000-2-2-2-2-2-2-2-2-2-2-2222-22222220000200000000-2-20000000000000000
χ7122222222-2-2-2222-220000-22222-20000000000-2-200000000000000-2-2-2-2-2-2-2-2222-2-2-22-200002-2-2-2-2200000000002200000000000000
χ7222222222-2-2-2222-220000-2-2-2-2-2-200000000002200000000000000-2-2-2-2-2-2-2-2222-2-2-22-200002222220000000000-2-200000000000000
χ7322222222-2-2-2-2-2-2-2-200002000020000000000002-22-20000000000-2-2-2-2-2-2-2-2222222220000-20000-2000000000000-22-220000000000
χ7422222222-2-2-2-2-2-2-2-20000200002000000000000-22-220000000000-2-2-2-2-2-2-2-2222222220000-20000-20000000000002-22-20000000000
χ752222-2-2-2-22-22000-202-22-200000022−2−222−2−2000000002−22−2000000-2-2-2-22222-22-200020-22-22000000−2−222−2−22200000000−22−22000000
χ762222-2-2-2-22-22000-202-22-2000000−2−222−2−22200000000−22−22000000-2-2-2-22222-22-200020-22-2200000022−2−222−2−2000000002−22−2000000
χ772222-2-2-2-22-22000-20-22-2200000022−2−222−2−200000000−22−22000000-2-2-2-22222-22-2000202-22-2000000−2−222−2−222000000002−22−2000000
χ782222-2-2-2-22-22000-20-22-22000000−2−222−2−222000000002−22−2000000-2-2-2-22222-22-2000202-22-200000022−2−222−2−200000000−22−22000000
χ7922-2-2-222-200022-20-2000002-22-20i2−i2i2−i2i2−i2i2−i2000000000000i2−i2i2−i200-2-2222-2-22000-2-220200000-22-220−i2i2−i2i2−i2i2−i2i2000000000000−i2i2−i2i200
χ8022-2-2-222-200022-20-2000002-22-20−i2i2−i2i2−i2i2−i2i2000000000000−i2i2−i2i200-2-2222-2-22000-2-220200000-22-220i2−i2i2−i2i2−i2i2−i2000000000000i2−i2i2−i200
χ8122-2-2-222-200022-20-200000-22-220i2−i2i2−i2i2−i2i2−i2000000000000−i2i2−i2i200-2-2222-2-22000-2-2202000002-22-20−i2i2−i2i2−i2i2−i2i2000000000000i2−i2i2−i200
χ8222-2-2-222-200022-20-200000-22-220−i2i2−i2i2−i2i2−i2i2000000000000i2−i2i2−i200-2-2222-2-22000-2-2202000002-22-20i2−i2i2−i2i2−i2i2−i2000000000000−i2i2−i2i200
χ832-22-2-22-220002-220-2000002i−2i−2i2i0i2−i2i2−i2−i2i2−i2i2000000000000−222−200-22-222-22-2000-22-20200000−2i2i2i−2i0−i2i2−i2i2i2−i2i2−i20000000000002−2−2200
χ842-22-2-22-220002-220-2000002i−2i−2i2i0−i2i2−i2i2i2−i2i2−i20000000000002−2−2200-22-222-22-2000-22-20200000−2i2i2i−2i0i2−i2i2−i2−i2i2−i2i2000000000000−222−200
χ852-22-2-22-220002-220-200000−2i2i2i−2i0i2−i2i2−i2−i2i2−i2i20000000000002−2−2200-22-222-22-2000-22-202000002i−2i−2i2i0−i2i2−i2i2i2−i2i2−i2000000000000−222−200
χ862-22-2-22-220002-220-200000−2i2i2i−2i0−i2i2−i2i2i2−i2i2−i2000000000000−222−200-22-222-22-2000-22-202000002i−2i−2i2i0i2−i2i2−i2−i2i2−i2i20000000000002−2−2200
χ872-2-2222-2-222-2-222-2-222-2-220000-200000000-220000000000000000-222-2-2-222-2-222-2-222-2-222-200002000000002-20000000000000000
χ882-2-2222-2-222-2-222-2-2-2-22220000-2000000002-20000000000000000-222-2-2-222-2-222-2-22222-2-2-20000200000000-220000000000000000
χ892-2-2222-2-2-2-222-2-222000022i2i−2i−2i-20000000000−2i2i00000000000000-222-2-2-22222-2-222-2-20000-2−2i−2i2i2i200000000002i−2i00000000000000
χ902-2-2222-2-2-2-222-2-22200002−2i−2i2i2i-200000000002i−2i00000000000000-222-2-2-22222-2-222-2-20000-22i2i−2i−2i20000000000−2i2i00000000000000
χ912-2-2222-2-2-2-22-2222-20000-2000020000000000002i−2i−2i2i0000000000-222-2-2-22222-22-2-2-22000020000-2000000000000−2i2i2i−2i0000000000
χ922-2-2222-2-2-2-22-2222-20000-200002000000000000−2i2i2i−2i0000000000-222-2-2-22222-22-2-2-22000020000-20000000000002i−2i−2i2i0000000000
χ932-2-22-2-2222-2-2000202-2-2200000022−2−2−2−222000000002−2−22000000-222-222-2-2-222000-20-222-2000000−2−22222−2−200000000−222−2000000
χ942-2-22-2-2222-2-2000202-2-22000000−2−22222−2−200000000−222−2000000-222-222-2-2-222000-20-222-200000022−2−2−2−222000000002−2−22000000
χ952-2-22-2-2222-2-200020-222-200000022−2−2−2−22200000000−222−2000000-222-222-2-2-222000-202-2-22000000−2−22222−2−2000000002−2−22000000
χ962-2-22-2-2222-2-200020-222-2000000−2−22222−2−2000000002−2−22000000-222-222-2-2-222000-202-2-2200000022−2−2−2−22200000000−222−2000000
χ974444-4-4-4-4-44-400040000000000000000000000000000000000000-4-4-4-444444-44000-40000000000000000000000000000000000000
χ9844-4-44-4-440000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000-4-444-444-4000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ9944-4-44-4-44000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000-4-444-444-40000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ10044-4-4-444-4000-4-4404000000000000000000000000000000000000-4-4444-4-4400044-40-4000000000000000000000000000000000000
χ1014-44-44-44-40000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000-44-44-44-44000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ1024-44-44-44-4000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000-44-44-44-440000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ1034-44-4-44-44000-44-404000000000000000000000000000000000000-44-444-44-40004-440-4000000000000000000000000000000000000
χ1044-4-44-4-444-444000-40000000000000000000000000000000000000-444-444-4-44-4-400040000000000000000000000000000000000000

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