Finite Group Databasebeta

← Group #10591164

Character table — Group #10591164

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11112222222222222222222222222244444444444444444444446666666666666666666666662424242424247272
order12222233444466666666661212121212121212366666666612121212121212121212121288888888242424242424242424242424242424242466121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ51111-1-1111-1-1111-1-1-1-1111111-1-1-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11-1
χ61111-1-1111-1-1111-1-1-1-1111111-1-1-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-11
χ71111-1-1111-1-1111-1-1-1-1111111-1-1-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-111-1-1-11
χ81111-1-1111-1-1111-1-1-1-1111111-1-1-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-1111-1
χ922222222-2-2-2-22222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ102222222-12222222222-12-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-100
χ112222222-12222222222-12-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2111100
χ122222222-1-2-2-2-2222222-12-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111100000000000000000000000000−i3i3−i3i300
χ132222222-1-2-2-2-2222222-12-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111100000000000000000000000000i3−i3i3−i300
χ14222222-122222-1-1-1-1-1-12-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ15222222-122222-1-1-1-1-1-12-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000
χ16222222-12-2-2-2-2-1-1-1-1-1-12-12211111111-122-1-1-1-1-1-1-1-2-2-2-211111111000000003333−3−3−3−33333−3−3−3−300000000
χ17222222-12-2-2-2-2-1-1-1-1-1-12-12211111111-122-1-1-1-1-1-1-1-2-2-2-21111111100000000−3−3−3−33333−3−3−3−3333300000000
χ182222-2-222-222-222-2-2-2-22222-2-22222-2-22-2-222-2-2-2-22-2-222-2-2-2-2222200000000000000000000000000000000
χ192222-2-22-12-2-2222-2-2-2-2-12-1-122-2-2-2-222-111-1-11111-1-1-111-1-1-1-111110000000000000000000000002-2-1-11100
χ202222-2-22-12-2-2222-2-2-2-2-12-1-122-2-2-2-222-111-1-11111-1-1-111-1-1-1-11111000000000000000000000000-2211-1-100
χ212222-2-22-1-222-222-2-2-2-2-12-1-1-2-22222-2-2-111-1-11111-111-1-11111-1-1-1-100000000000000000000000000−i3i3i3−i300
χ222222-2-22-1-222-222-2-2-2-2-12-1-1-2-22222-2-2-111-1-11111-111-1-11111-1-1-1-100000000000000000000000000i3−i3−i3i300
χ232222-2-2-122-2-22-1-111112-122-1-11111-1-1-1-2-2-1-11111-122-2-2-1-1-1-111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000
χ242222-2-2-122-2-22-1-111112-122-1-11111-1-1-1-2-2-1-11111-122-2-2-1-1-1-11111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000
χ252222-2-2-12-222-2-1-111112-12211-1-1-1-111-1-2-2-1-11111-1-2-2221111-1-1-1-1000000003333−3−3−3−3−3−3−3−3333300000000
χ262222-2-2-12-222-2-1-111112-12211-1-1-1-111-1-2-2-1-11111-1-2-2221111-1-1-1-100000000−3−3−3−333333333−3−3−3−300000000
χ2722-2-2002202i−2i02-200002-2-2-2002i2i−2i−2i002002-20000-2002i−2i00002i2i−2i−2i22−2−2−i2−i2i2i222−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000
χ2822-2-2002202i−2i02-200002-2-2-2002i2i−2i−2i002002-20000-2002i−2i00002i2i−2i−2i−2−222i2i2−i2−i2−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000
χ2922-2-200220−2i2i02-200002-2-2-200−2i−2i2i2i002002-20000-200−2i2i0000−2i−2i2i2i22−2−2i2i2−i2−i222−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000
χ3022-2-200220−2i2i02-200002-2-2-200−2i−2i2i2i002002-20000-200−2i2i0000−2i−2i2i2i−2−222−i2−i2i2i2−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000
χ3122-2-200-1202i−2i0-11−i3−i3i3i321-2-23−3−i−iii3−3-100-11−i3−i3i3i31002i−2i33−3−3−i−iii22−2−2−i2−i2i2i2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000000
χ3222-2-200-1202i−2i0-11−i3−i3i3i321-2-23−3−i−iii3−3-100-11−i3−i3i3i31002i−2i33−3−3−i−iii−2−222i2i2−i2−i2−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000000
χ3322-2-200-1202i−2i0-11i3i3−i3−i321-2-2−33−i−iii−33-100-11i3i3−i3−i31002i−2i−3−333−i−iii22−2−2−i2−i2i2i2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000000
χ3422-2-200-1202i−2i0-11i3i3−i3−i321-2-2−33−i−iii−33-100-11i3i3−i3−i31002i−2i−3−333−i−iii−2−222i2i2−i2−i2−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000000
χ3522-2-200-120−2i2i0-11−i3−i3i3i321-2-2−33ii−i−i−33-100-11−i3−i3i3i3100−2i2i−3−333ii−i−i22−2−2i2i2−i2−i2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000000
χ3622-2-200-120−2i2i0-11−i3−i3i3i321-2-2−33ii−i−i−33-100-11−i3−i3i3i3100−2i2i−3−333ii−i−i−2−222−i2−i2i2i2−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000000
χ3722-2-200-120−2i2i0-11i3i3−i3−i321-2-23−3ii−i−i3−3-100-11i3i3−i3−i3100−2i2i33−3−3ii−i−i22−2−2i2i2−i2−i2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000000
χ3822-2-200-120−2i2i0-11i3i3−i3−i321-2-23−3ii−i−i3−3-100-11i3i3−i3−i3100−2i2i33−3−3ii−i−i−2−222−i2−i2i2i2−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000000
χ392-22-20022200-2-2-20000-222-2220000-2-2200-2-2000022-2002-22-2000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i00000000
χ402-22-20022200-2-2-20000-222-2220000-2-2200-2-2000022-2002-22-200000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i00000000
χ412-22-20022-2002-2-20000-222-2-2-2000022200-2-200002-2200-22-2200002-22-200002-22-22-22-20000000000000000
χ422-22-20022-2002-2-20000-222-2-2-2000022200-2-200002-2200-22-220000-22-220000-22-22-22-220000000000000000
χ432-22-200-12200-211−i3i3−i3i3-2-12-2-1-1−i3i3−i3i311-10011−i3i3−i3i3-12-200-11-11−i3i3−i3i300002i−2i2i−2i3−33−3−33−33−ii−ii−ii−ii00000000
χ442-22-200-12200-211−i3i3−i3i3-2-12-2-1-1−i3i3−i3i311-10011−i3i3−i3i3-12-200-11-11−i3i3−i3i30000−2i2i−2i2i−33−333−33−3i−ii−ii−ii−i00000000
χ452-22-200-12200-211i3−i3i3−i3-2-12-2-1-1i3−i3i3−i311-10011i3−i3i3−i3-12-200-11-11i3−i3i3−i300002i−2i2i−2i−33−333−33−3−ii−ii−ii−ii00000000
χ462-22-200-12200-211i3−i3i3−i3-2-12-2-1-1i3−i3i3−i311-10011i3−i3i3−i3-12-200-11-11i3−i3i3−i30000−2i2i−2i2i3−33−3−33−33i−ii−ii−ii−i00000000
χ472-22-200-12-200211−i3i3−i3i3-2-12-211i3−i3i3−i3-1-1-10011−i3i3−i3i3-1-22001-11-1i3−i3i3−i32-22-20000-11-11-11-11−i3i3−i3i3i3−i3i3−i300000000
χ482-22-200-12-200211−i3i3−i3i3-2-12-211i3−i3i3−i3-1-1-10011−i3i3−i3i3-1-22001-11-1i3−i3i3−i3-22-2200001-11-11-11-1i3−i3i3−i3−i3i3−i3i300000000
χ492-22-200-12-200211i3−i3i3−i3-2-12-211−i3i3−i3i3-1-1-10011i3−i3i3−i3-1-22001-11-1−i3i3−i3i32-22-20000-11-11-11-11i3−i3i3−i3−i3i3−i3i300000000
χ502-22-200-12-200211i3−i3i3−i3-2-12-211−i3i3−i3i3-1-1-10011i3−i3i3−i3-1-22001-11-1−i3i3−i3i3-22-2200001-11-11-11-1−i3i3−i3i3i3−i3i3−i300000000
χ512-2-222-2220000-222-2-22-2-2-220000000022-2-222-2-22-20000000000002−2−22−222−22−2−222−2−22−222−2−222−200000000
χ522-2-222-2220000-222-2-22-2-2-220000000022-2-222-2-22-2000000000000−222−22−2−22−222−2−222−22−2−222−2−2200000000
χ532-2-222-2-1200001-1-111-1-21-223−33−3−33−33-12-21-1-111-1100003−3−333−3−332−2−22−222−2ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ542-2-222-2-1200001-1-111-1-21-223−33−3−33−33-12-21-1-111-1100003−3−333−3−33−222−22−2−22−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ552-2-222-2-1200001-1-111-1-21-22−33−333−33−3-12-21-1-111-110000−333−3−333−32−2−22−222−2ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ562-2-222-2-1200001-1-111-1-21-22−33−333−33−3-12-21-1-111-110000−333−3−333−3−222−22−2−22−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ572-2-22-22220000-22-222-2-2-2-22000000002-22-22-222-2-20000000000002−2−222−2−222−2−222−2−222−2−222−2−2200000000
χ582-2-22-22220000-22-222-2-2-2-22000000002-22-22-222-2-2000000000000−222−2−222−2−222−2−222−2−222−2−222−200000000
χ592-2-22-22-1200001-11-1-11-21-223−3−333−3−33-1-221-11-1-11100003−3−33−333−32−2−222−2−22ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ700000000
χ602-2-22-22-1200001-11-1-11-21-223−3−333−3−33-1-221-11-1-11100003−3−33−333−3−222−2−222−2−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ700000000
χ612-2-22-22-1200001-11-1-11-21-22−333−3−333−3-1-221-11-1-1110000−333−33−3−332−2−222−2−22ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300000000
χ622-2-22-22-1200001-11-1-11-21-22−333−3−333−3-1-221-11-1-1110000−333−33−3−33−222−2−222−2−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300000000
χ63444444-2-24444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-21111111-2-2-2-21111111100000000000000000000000000000000
χ64444444-2-2-4-4-4-4-2-2-2-2-2-2-2-2-2-2222222221-2-211111112222-1-1-1-1-1-1-1-100000000000000000000000000000000
χ654444-4-4-2-24-4-44-2-22222-2-2-2-2-2-22222-2-212211-1-1-1-11-2-2221111-1-1-1-100000000000000000000000000000000
χ664444-4-4-2-2-444-4-2-22222-2-2-2-222-2-2-2-22212211-1-1-1-1122-2-2-1-1-1-1111100000000000000000000000000000000
χ6744-4-4004-204i−4i04-40000-2-422004i4i−4i−4i00-200-220000200−2i2i0000−2i−2i2i2i00000000000000000000000000000000
χ6844-4-4004-20−4i4i04-40000-2-42200−4i−4i4i4i00-200-2200002002i−2i00002i2i−2i−2i00000000000000000000000000000000
χ6944-4-400-2-204i−4i0-22−2i3−2i32i32i3-222223−23−2i−2i2i2i23−231001-1i3i3−i3−i3-100−2i2i−3−333ii−i−i00000000000000000000000000000000
χ7044-4-400-2-204i−4i0-222i32i3−2i3−2i3-2222−2323−2i−2i2i2i−23231001-1−i3−i3i3i3-100−2i2i33−3−3ii−i−i00000000000000000000000000000000
χ7144-4-400-2-20−4i4i0-22−2i3−2i32i32i3-2222−23232i2i−2i−2i−23231001-1i3i3−i3−i3-1002i−2i33−3−3−i−iii00000000000000000000000000000000
χ7244-4-400-2-20−4i4i0-222i32i3−2i3−2i3-222223−232i2i−2i−2i23−231001-1−i3−i3i3i3-1002i−2i−3−333−i−iii00000000000000000000000000000000
χ734-44-4004-2400-4-4-4000024-22440000-4-4-200220000-2-2200-22-22000000000000000000000000000000000000
χ744-44-4004-2-4004-4-4000024-22-4-4000044-200220000-22-2002-22-2000000000000000000000000000000000000
χ754-44-400-2-2400-422−2i32i3−2i32i32-2-22-2-2−2i32i3−2i32i322100-1-1i3−i3i3−i31-22001-11-1i3−i3i3−i300000000000000000000000000000000
χ764-44-400-2-2400-4222i3−2i32i3−2i32-2-22-2-22i3−2i32i3−2i322100-1-1−i3i3−i3i31-22001-11-1−i3i3−i3i300000000000000000000000000000000
χ774-44-400-2-2-400422−2i32i3−2i32i32-2-22222i3−2i32i3−2i3-2-2100-1-1i3−i3i3−i312-200-11-11−i3i3−i3i300000000000000000000000000000000
χ784-44-400-2-2-4004222i3−2i32i3−2i32-2-2222−2i32i3−2i32i3-2-2100-1-1−i3i3−i3i312-200-11-11i3−i3i3−i300000000000000000000000000000000
χ794-4-444-44-20000-444-4-442-42-200000000-2-222-2-222-2200000000000000000000000000000000000000000000
χ804-4-444-4-2-200002-2-222-2222-223−2323−23−2323−23231-22-111-1-11-10000−333−3−333−300000000000000000000000000000000
χ814-4-444-4-2-200002-2-222-2222-2−2323−232323−2323−231-22-111-1-11-100003−3−333−3−3300000000000000000000000000000000
χ824-4-44-444-20000-44-444-42-42-200000000-22-22-22-2-22200000000000000000000000000000000000000000000
χ834-4-44-44-2-200002-22-2-22222-223−23−232323−23−232312-2-11-111-1-10000−333−33−3−3300000000000000000000000000000000
χ844-4-44-44-2-200002-22-2-22222-2−232323−23−232323−2312-2-11-111-1-100003−3−33−333−300000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.