Finite Group Databasebeta

← Group #10848875

Character table — Group #10848875

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222222222222444444444444444444444444444444444444448888888888888888888888242424242424242448484848
order122222344444444666121212121212121212121212444444444444446612121212121212121212121212121212121212121212246688881212121212122424242424242424224444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111-1-11-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ61111111111111111111111111111111-1-11-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ71111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ81111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ91111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-111-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11-111-1-11-11-11-1
χ101111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-111-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-11-1-111-11-11-11
χ111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-111-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-111111-111-1-11-1-11-11
χ121111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-111-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-1-111-111-11-1
χ131111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-111111-1-1-1111-1-111-1
χ141111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1111-1-1-111-1-11
χ151111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-11-1-1-1111-11-1-11
χ161111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1-1111-1-1-11-111-1
χ17222222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2200-2000000000022-2-222-2-200000000000000000000000000000000000000002-22-2000000
χ18222222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2200-2000000000022-2-222-2-20000000000000000000000000000000000000000-22-22000000
χ192222222-2-222-2-2-2-2222-2-2-2-22222-2-2-2-2-2002000000000022-2-2-2-22200000000000000000000000000000000000000002-2-22000000
χ202222222-2-222-2-2-2-2222-2-2-2-22222-2-2-2-2-2002000000000022-2-2-2-2220000000000000000000000000000000000000000-222-2000000
χ21222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-1-1-2-2-2-2-1-1-1-1-1-111111111000000000000
χ23222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-22-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2-2-211111111111111000000000000
χ24222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-22-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2112222111111-1-1-1-1-1-1-1-1000000000000
χ25222222-1-2-2-2-22222-1-1-111111111-1-1-1-1-222-2222222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111-2-21122-2-2-1-1-1-111-1-1-1-11111000000000000
χ26222222-1-2-2-2-22222-1-1-111111111-1-1-1-1-222-222-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-1-2-211-2-222-1-1-1-1111111-1-1-1-1000000000000
χ27222222-1-2-2-2-22222-1-1-111111111-1-1-1-1-2-2-2-2-2-22222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-11111111122-1-1-2-2221111-1-11111-1-1-1-1000000000000
χ28222222-1-2-2-2-22222-1-1-111111111-1-1-1-1-2-2-2-2-2-2-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-122-1-122-2-21111-1-1-1-1-1-11111000000000000
χ292222-2-222222-222-2222222222222222-200-20000000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000220000-2-20000
χ302222-2-222222-222-2222222222222222-200-20000000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000-2-20000220000
χ312222-2-2222-2-22-2-222222222-2-2-2-2-2-2-2-2-2222-2-200000000-2-222-2-22200000000000000002-222000022-2-2-2-200000000000000000000
χ322222-2-2222-2-22-2-222222222-2-2-2-2-2-2-2-2-2-2-222200000000-2-222-2-2220000000000000000-22-2-20000-2-2222200000000000000000000
χ332222-2-22-2-2222-2-22222-2-2-2-22222-2-2-2-2222-2-2-200000000-2-22222-2-20000000000000000-22-2-2000022-2-22200000000000000000000
χ342222-2-22-2-2222-2-22222-2-2-2-22222-2-2-2-22-2-2-22200000000-2-22222-2-200000000000000002-2220000-2-222-2-200000000000000000000
χ352222-2-22-2-2-2-2-222-2222-2-2-2-2-2-2-2-2222220020000000000-2-2-2-22222000000000000000000000000000000000000002-20000-220000
χ362222-2-22-2-2-2-2-222-2222-2-2-2-2-2-2-2-2222220020000000000-2-2-2-2222200000000000000000000000000000000000000-2200002-20000
χ372222-2-2-122-2-22-2-22-1-1-1-1-1-1-111111111-2222-2-20000000011-1-111-1-13333−3−3−3−33333−3−3−3−32-2-1-10000-1-1111133−3−333−3−3000000000000
χ382222-2-2-122-2-22-2-22-1-1-1-1-1-1-111111111-2222-2-20000000011-1-111-1-1−3−3−3−33333−3−3−3−333332-2-1-10000-1-11111−3−333−3−333000000000000
χ392222-2-2-122-2-22-2-22-1-1-1-1-1-1-111111111-2-2-22220000000011-1-111-1-13333−3−3−3−33333−3−3−3−3-2211000011-1-1-1-1−3−333−3−333000000000000
χ402222-2-2-122-2-22-2-22-1-1-1-1-1-1-111111111-2-2-22220000000011-1-111-1-1−3−3−3−33333−3−3−3−33333-2211000011-1-1-1-133−3−333−3−3000000000000
χ412222-2-2-1-2-2222-2-22-1-1-11111-1-1-1-11111222-2-2-20000000011-1-1-1-1113333−3−3−3−3−3−3−3−33333-22110000-1-111-1-133−3−3−3−333000000000000
χ422222-2-2-1-2-2222-2-22-1-1-11111-1-1-1-11111222-2-2-20000000011-1-1-1-111−3−3−3−333333333−3−3−3−3-22110000-1-111-1-1−3−33333−3−3000000000000
χ432222-2-2-1-2-2222-2-22-1-1-11111-1-1-1-111112-2-2-2220000000011-1-1-1-1113333−3−3−3−3−3−3−3−333332-2-1-1000011-1-111−3−33333−3−3000000000000
χ442222-2-2-1-2-2222-2-22-1-1-11111-1-1-1-111112-2-2-2220000000011-1-1-1-111−3−3−3−333333333−3−3−3−32-2-1-1000011-1-11133−3−3−3−333000000000000
χ452-2-222-22000022-2-22-2-20000000022-2-202i−2i02i−2i00002i2i−2i−2i2-22-20000000000002i2i−2i−2i2i2i−2i−2i0000002-22i−2i2i−2i0000002-22-2000000000000
χ462-2-222-22000022-2-22-2-20000000022-2-202i−2i02i−2i0000−2i−2i2i2i2-22-2000000000000−2i−2i2i2i−2i−2i2i2i000000-222i−2i2i−2i000000-22-22000000000000
χ472-2-222-22000022-2-22-2-20000000022-2-20−2i2i0−2i2i00002i2i−2i−2i2-22-20000000000002i2i−2i−2i2i2i−2i−2i000000-22−2i2i−2i2i000000-22-22000000000000
χ482-2-222-22000022-2-22-2-20000000022-2-20−2i2i0−2i2i0000−2i−2i2i2i2-22-2000000000000−2i−2i2i2i−2i−2i2i2i0000002-2−2i2i−2i2i0000002-22-2000000000000
χ492-2-222-2-1000022-2-2-11133−3−333−3−3-1-11102i−2i02i−2i00002i2i−2i−2i-11-113−33−3−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii00−i3i3002-2−ii−ii−i3i33−33−3-11-11000000000000
χ502-2-222-2-1000022-2-2-11133−3−333−3−3-1-11102i−2i02i−2i0000−2i−2i2i2i-11-113−33−3i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i00−i3i300-22−ii−ii−i3i3−33−331-11-1000000000000
χ512-2-222-2-1000022-2-2-11133−3−333−3−3-1-1110−2i2i0−2i2i00002i2i−2i−2i-11-113−33−3−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii00i3−i300-22i−ii−ii3−i3−33−331-11-1000000000000
χ522-2-222-2-1000022-2-2-11133−3−333−3−3-1-1110−2i2i0−2i2i0000−2i−2i2i2i-11-113−33−3i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i00i3−i3002-2i−ii−ii3−i33−33−3-11-11000000000000
χ532-2-222-2-1000022-2-2-111−3−333−3−333-1-11102i−2i02i−2i00002i2i−2i−2i-11-11−33−33i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii00i3−i3002-2−ii−iii3−i3−33−33-11-11000000000000
χ542-2-222-2-1000022-2-2-111−3−333−3−333-1-11102i−2i02i−2i0000−2i−2i2i2i-11-11−33−33−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i00i3−i300-22−ii−iii3−i33−33−31-11-1000000000000
χ552-2-222-2-1000022-2-2-111−3−333−3−333-1-1110−2i2i0−2i2i00002i2i−2i−2i-11-11−33−33i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii00−i3i300-22i−ii−i−i3i33−33−31-11-1000000000000
χ562-2-222-2-1000022-2-2-111−3−333−3−333-1-1110−2i2i0−2i2i0000−2i−2i2i2i-11-11−33−33−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i00−i3i3002-2i−ii−i−i3i3−33−33-11-11000000000000
χ572-2-22-22200002-22-22-2-200000000-2-22202i−2i0−2i2i2i2i−2i−2i0000-222-200002i2i−2i−2i−2i−2i2i2i0000000000002-2002i−2i−2i2i00-222-20000000000000000
χ582-2-22-22200002-22-22-2-200000000-2-22202i−2i0−2i2i−2i−2i2i2i0000-222-20000−2i−2i2i2i2i2i−2i−2i000000000000-22002i−2i−2i2i002-2-220000000000000000
χ592-2-22-22200002-22-22-2-200000000-2-2220−2i2i02i−2i2i2i−2i−2i0000-222-200002i2i−2i−2i−2i−2i2i2i000000000000-2200−2i2i2i−2i002-2-220000000000000000
χ602-2-22-22200002-22-22-2-200000000-2-2220−2i2i02i−2i−2i−2i2i2i0000-222-20000−2i−2i2i2i2i2i−2i−2i0000000000002-200−2i2i2i−2i00-222-20000000000000000
χ612-2-22-22-100002-22-2-11133−3−3−3−33311-1-102i−2i0−2i2i2i2i−2i−2i00001-1-11−333−3−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i300−i3i32-200−iii−ii3−i31-1-113−3−33000000000000
χ622-2-22-22-100002-22-2-11133−3−3−3−33311-1-102i−2i0−2i2i−2i−2i2i2i00001-1-11−333−3ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i300−i3i3-2200−iii−ii3−i3-111-1−333−3000000000000
χ632-2-22-22-100002-22-2-11133−3−3−3−33311-1-10−2i2i02i−2i2i2i−2i−2i00001-1-11−333−3−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i300i3−i3-2200i−i−ii−i3i3-111-1−333−3000000000000
χ642-2-22-22-100002-22-2-11133−3−3−3−33311-1-10−2i2i02i−2i−2i−2i2i2i00001-1-11−333−3ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i300i3−i32-200i−i−ii−i3i31-1-113−3−33000000000000
χ652-2-22-22-100002-22-2-111−3−33333−3−311-1-102i−2i0−2i2i2i2i−2i−2i00001-1-113−3−33−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i300i3−i32-200−iii−i−i3i31-1-11−333−3000000000000
χ662-2-22-22-100002-22-2-111−3−33333−3−311-1-102i−2i0−2i2i−2i−2i2i2i00001-1-113−3−33ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i300i3−i3-2200−iii−i−i3i3-111-13−3−33000000000000
χ672-2-22-22-100002-22-2-111−3−33333−3−311-1-10−2i2i02i−2i2i2i−2i−2i00001-1-113−3−33−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i300−i3i3-2200i−i−iii3−i3-111-13−3−33000000000000
χ682-2-22-22-100002-22-2-111−3−33333−3−311-1-10−2i2i02i−2i−2i−2i2i2i00001-1-113−3−33ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i300−i3i32-200i−i−iii3−i31-1-11−333−3000000000000
χ69444444-244-4-4-4-4-4-4-2-2-2-2-2-2-222222222400-40000000000-2-222-2-22200000000000000000000000000000000000000000000000000
χ70444444-2-4-444-4-4-4-4-2-2-22222-2-2-2-22222-40040000000000-2-22222-2-200000000000000000000000000000000000000000000000000
χ714444-4-4-24444-444-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-400-400000000002222222200000000000000000000000000000000000000000000000000
χ724444-4-4-2-4-4-4-4-444-4-2-2-222222222-2-2-2-2400400000000002222-2-2-2-200000000000000000000000000000000000000000000000000
χ7344-4-40044-4000000-44-44-44-4000000000000002-22-22-22-2000000002-22-22-22-22-22-22-22-20000000000000000000000000000000000
χ7444-4-40044-4000000-44-44-44-400000000000000-22-22-22-2200000000-22-22-22-22-22-22-22-220000000000000000000000000000000000
χ7544-4-4004-44000000-44-4-44-44000000000000002-22-2-22-22000000002-22-22-22-2-22-22-22-220000000000000000000000000000000000
χ7644-4-4004-44000000-44-4-44-4400000000000000-22-222-22-200000000-22-22-22-222-22-22-22-20000000000000000000000000000000000
χ7744-4-400-24-40000002-22-22-2223−2323−2323−2323−230000002-22-22-22-200000000−1+31−3−1+31−3−1−31+3−1−31+3−1+31−3−1+31−3−1−31+3−1−31+30000000000000000000000000000000000
χ7844-4-400-24-40000002-22-22-2223−2323−2323−2323−23000000-22-22-22-22000000001−3−1+31−3−1+31+3−1−31+3−1−31−3−1+31−3−1+31+3−1−31+3−1−30000000000000000000000000000000000
χ7944-4-400-24-40000002-22-22-22−2323−2323−2323−23230000002-22-22-22-200000000−1−31+3−1−31+3−1+31−3−1+31−3−1−31+3−1−31+3−1+31−3−1+31−30000000000000000000000000000000000
χ8044-4-400-24-40000002-22-22-22−2323−2323−2323−2323000000-22-22-22-22000000001+3−1−31+3−1−31−3−1+31−3−1+31+3−1−31+3−1−31−3−1+31−3−1+30000000000000000000000000000000000
χ8144-4-400-2-440000002-222-22-223−2323−23−2323−23230000002-22-2-22-2200000000−1−31+3−1−31+3−1+31−3−1+31−31+3−1−31+3−1−31−3−1+31−3−1+30000000000000000000000000000000000
χ8244-4-400-2-440000002-222-22-223−2323−23−2323−2323000000-22-222-22-2000000001+3−1−31+3−1−31−3−1+31−3−1+3−1−31+3−1−31+3−1+31−3−1+31−30000000000000000000000000000000000
χ8344-4-400-2-440000002-222-22-2−2323−232323−2323−230000002-22-2-22-2200000000−1+31−3−1+31−3−1−31+3−1−31+31−3−1+31−3−1+31+3−1−31+3−1−30000000000000000000000000000000000
χ8444-4-400-2-440000002-222-22-2−2323−232323−2323−23000000-22-222-22-2000000001−3−1+31−3−1+31+3−1−31+3−1−3−1+31−3−1+31−3−1−31+3−1−31+30000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.