Finite Group Databasebeta

← Group #11781810

Character table — Group #11781810

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1111222222222222222244444444444444444444444444444444444444444444444444444444444444424242424242424242424242448484848484872727272
order1222334444666666121212123466688881212121212121212121212121212121212121212121224242424242424242424242424242424242424242424242424242424242424244488121212122424242444121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-111-1-1
χ61111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1-111-1-111
χ71111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-111-1-1-1-111
χ81111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-1
χ922222222-2-222222222222-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000
χ1022222222-2-222222222222-2222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222222222220000000000000000000000
χ11222222-2-222222222-2-2-2-22-2222000022-2-222-2-22222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000002-20022-2-200000000000000
χ12222222-2-222222222-2-2-2-22-2222000022-2-222-2-22222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000-2200-2-22200000000000000
χ13222222-2-2-2-2222222-2-2-2-2222220000-2-222-2-222-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000002i−2i00002i2i−2i−2i0000000000
χ14222222-2-2-2-2222222-2-2-2-2222220000-2-222-2-222-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000−2i2i0000−2i−2i2i2i0000000000
χ1522222-1222222-1-1-12-1-1-1-1-12-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ1622222-1222222-1-1-12-1-1-1-1-12-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ1722222-1222222-1-1-12-1-1-1-1-12-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-111111111-2-2-2-211111111-2-2-2-21111111122-2-2-1-1-1-111110000000000
χ1822222-1222222-1-1-12-1-1-1-1-12-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-111111111-2-2-2-211111111-2-2-2-211111111-2-2221111-1-1-1-10000000000
χ1922222-122-2-222-1-1-12-1-1-1-1-1-2-1-1-122-2-2-2-2-2-211111111111122-1-1-1-1-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-2111111110000−i3i3−i3i3−i3i3−i3i30000000000
χ2022222-122-2-222-1-1-12-1-1-1-1-1-2-1-1-122-2-2-2-2-2-211111111111122-1-1-1-1-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-2111111110000i3−i3i3−i3i3−i3i3−i30000000000
χ2122222-122-2-222-1-1-12-1-1-1-1-1-2-1-1-1-2-222-2-2-2-211111111111122-1-1-1-11111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000
χ2222222-122-2-222-1-1-12-1-1-1-1-1-2-1-1-1-2-222-2-2-2-211111111111122-1-1-1-11111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000
χ2322222-1-2-22222-1-1-121111-1-2-1-1-1000022-2-2-1-111-1-1-1-11111-2-2111133−3−333−3−300003333−3−3−3−300003333−3−3−3−32-200-1-1113−3−330000000000
χ2422222-1-2-22222-1-1-121111-1-2-1-1-1000022-2-2-1-111-1-1-1-11111-2-2111133−3−333−3−300003333−3−3−3−300003333−3−3−3−3-220011-1-1−333−30000000000
χ2522222-1-2-22222-1-1-121111-1-2-1-1-1000022-2-2-1-111-1-1-1-11111-2-21111−3−333−3−3330000−3−3−3−333330000−3−3−3−333332-200-1-111−333−30000000000
χ2622222-1-2-22222-1-1-121111-1-2-1-1-1000022-2-2-1-111-1-1-1-11111-2-21111−3−333−3−3330000−3−3−3−333330000−3−3−3−33333-220011-1-13−3−330000000000
χ2722222-1-2-2-2-222-1-1-121111-12-1-1-10000-2-22211-1-11111-1-1-1-1-2-2111133−3−3−3−33300003333−3−3−3−30000−3−3−3−33333002i−2i−i3i3i3−i3−i−iii0000000000
χ2822222-1-2-2-2-222-1-1-121111-12-1-1-10000-2-22211-1-11111-1-1-1-1-2-2111133−3−3−3−33300003333−3−3−3−30000−3−3−3−3333300−2i2ii3−i3−i3i3ii−i−i0000000000
χ2922222-1-2-2-2-222-1-1-121111-12-1-1-10000-2-22211-1-11111-1-1-1-1-2-21111−3−33333−3−30000−3−3−3−3333300003333−3−3−3−3002i−2ii3−i3−i3i3−i−iii0000000000
χ3022222-1-2-2-2-222-1-1-121111-12-1-1-10000-2-22211-1-11111-1-1-1-1-2-21111−3−33333−3−30000−3−3−3−3333300003333−3−3−3−300−2i2i−i3i3i3−i3ii−i−i0000000000
χ312222-122222-1-1222-12222-12-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000
χ322222-122222-1-1222-12222-12-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-211110000
χ332222-122222-1-1222-12222-12-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111111111110000000000002-2-1-1110000
χ342222-122222-1-1222-12222-12-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111111111111000000000000-2211-1-10000
χ352222-1222-2-2-1-1222-12222-1-2-1-1-122-2-21111-2-2-2-211111111-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000000−i3i3−i3i30000
χ362222-1222-2-2-1-1222-12222-1-2-1-1-122-2-21111-2-2-2-211111111-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000000i3−i3i3−i30000
χ372222-1222-2-2-1-1222-12222-1-2-1-1-1-2-2221111-2-2-2-211111111-1-1-1-1-1-1-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-1-1-1-100000000000000−i3i3i3−i30000
χ382222-1222-2-2-1-1222-12222-1-2-1-1-1-2-2221111-2-2-2-211111111-1-1-1-1-1-1-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-1-1-1-100000000000000i3−i3−i3i30000
χ392-2-22222-200-2-22-2-2222-2-2202-2-22-20000000000000000002-222-2-22-22-2000022-2-222-2-222-2-2000000000000000000000000000000−i2i2−i2i2
χ402-2-22222-200-2-22-2-2222-2-2202-2-22-20000000000000000002-222-2-22-22-2000022-2-222-2-222-2-2000000000000000000000000000000i2−i2i2−i2
χ412-2-22222-200-2-22-2-2222-2-2202-2-2-220000000000000000002-222-2-2-22-220000-2-222-2-222-2-222000000000000000000000000000000−i2i2i2−i2
χ422-2-22222-200-2-22-2-2222-2-2202-2-2-220000000000000000002-222-2-2-22-220000-2-222-2-222-2-222000000000000000000000000000000i2−i2−i2i2
χ434444-24-4-444-2-2444-2-4-4-4-4-2-4-2-2-20000-2-22244-4-4-2-2-2-22222222222000000000000000000000000000000000000000000000000000000
χ444444-24-4-4-4-4-2-2444-2-4-4-4-4-24-2-2-2000022-2-2-4-4442222-2-2-2-2222222000000000000000000000000000000000000000000000000000000
χ454444-2-24444-2-2-2-2-2-2-2-2-2-2141114444-2-2-2-2-2-2-2-211111111-2-21111-2-2-2-2-2-2-2-2-2-2-2-211111111-2-2-2-2111111110000000000000000000000
χ464444-2-24444-2-2-2-2-2-2-2-2-2-214111-4-4-4-4-2-2-2-2-2-2-2-211111111-2-21111222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000000000
χ474444-2-244-4-4-2-2-2-2-2-2-2-2-2-21-411144-4-422222222-1-1-1-1-1-1-1-1-2-21111-2-2-2-22222-2-2-2-2111111112222-1-1-1-1-1-1-1-10000000000000000000000
χ484444-2-244-4-4-2-2-2-2-2-2-2-2-2-21-4111-4-44422222222-1-1-1-1-1-1-1-1-2-211112222-2-2-2-22222-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000000000
χ494444-2-2-4-444-2-2-2-2-2-222221-41110000-2-222-2-2221111-1-1-1-122-1-1-1-12323−23−232323−23−230000−3−3−3−333330000−3−3−3−333330000000000000000000000
χ504444-2-2-4-444-2-2-2-2-2-222221-41110000-2-222-2-2221111-1-1-1-122-1-1-1-1−23−232323−23−23232300003333−3−3−3−300003333−3−3−3−30000000000000000000000
χ514444-2-2-4-4-4-4-2-2-2-2-2-2222214111000022-2-222-2-2-1-1-1-1111122-1-1-1-12323−23−23−23−2323230000−3−3−3−3333300003333−3−3−3−30000000000000000000000
χ524444-2-2-4-4-4-4-2-2-2-2-2-2222214111000022-2-222-2-2-1-1-1-1111122-1-1-1-1−23−2323232323−23−2300003333−3−3−3−30000−3−3−3−333330000000000000000000000
χ5344-4-44400004-4-44-4-4000040-44-40022−220000000000000000000000000022−2222−220000000000002222−22−222222−22−222222−22−220000000000000000000000
χ5444-4-44400004-4-44-4-4000040-44-400−222200000000000000000000000000−2222−2222000000000000−22−222222−22−222222−22−2222220000000000000000000000
χ5544-4-44-200004-42-22-423−2323−23-202-220022−2200000000000000000023−2323−2300002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ230000000000002222−22−222ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ72ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ230000000000000000000000
χ5644-4-44-200004-42-22-423−2323−23-202-2200−222200000000000000000023−2323−230000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23000000000000−22−222222−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ230000000000000000000000
χ5744-4-44-200004-42-22-4−2323−2323-202-220022−22000000000000000000−2323−232300002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ70000000000002222−22−222ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ232ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ70000000000000000000000
χ5844-4-44-200004-42-22-4−2323−2323-202-2200−2222000000000000000000−2323−23230000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7000000000000−22−222222−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ70000000000000000000000
χ5944-4-4-240000-22-44-420000-202-220022−2200−2i32i300000000−2i3−2i32i32i3000000000022−2222−22i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6−2−222−2−222−2−2220000000000000000000000
χ6044-4-4-240000-22-44-420000-202-220022−22002i3−2i3000000002i32i3−2i3−2i3000000000022−2222−22−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−2−222−2−222−2−2220000000000000000000000
χ6144-4-4-240000-22-44-420000-202-2200−222200−2i32i300000000−2i3−2i32i32i30000000000−2222−2222−i6i6−i6i6−i6i6−i6i6−i6i6−i6i622−2−222−2−222−2−20000000000000000000000
χ6244-4-4-240000-22-44-420000-202-2200−2222002i3−2i3000000002i32i3−2i3−2i30000000000−2222−2222i6−i6i6−i6i6−i6i6−i6i6−i6i6−i622−2−222−2−222−2−20000000000000000000000
χ6344-4-4-2-20000-222-22223−2323−2310-11-10022−2200−2i32i300003i3i−3i−3ii3i3−i3−i300−33−3300002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23i6−i6i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ230000000000000000000000
χ6444-4-4-2-20000-222-22223−2323−2310-11-10022−22002i3−2i30000−3i−3i3i3i−i3−i3i3i300−33−3300002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23−i6i6−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ230000000000000000000000
χ6544-4-4-2-20000-222-22223−2323−2310-11-100−222200−2i32i300003i3i−3i−3ii3i3−i3−i300−33−330000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23−i6i6−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ230000000000000000000000
χ6644-4-4-2-20000-222-22223−2323−2310-11-100−2222002i3−2i30000−3i−3i3i3i−i3−i3i3i300−33−330000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23i6−i6i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ230000000000000000000000
χ6744-4-4-2-20000-222-222−2323−232310-11-10022−2200−2i32i30000−3i−3i3i3ii3i3−i3−i3003−33−300002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7i6−i6i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ70000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.