Finite Group Databasebeta

← Group #13149838

Character table — Group #13149838

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1122222222244444446666666666661212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order122344688121268122424242433666612122424242436666121212121212122424242424242424242424242424224422444444668812122424242466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111-11-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-111-1-111-1-111-1-1-1-11-11-111-1-1
χ61111111-1-1111-11-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-11111-1-111-1-1-1-1-11-11-1-111
χ71111111-1-1111-11-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-111-1-111111-11-1-1-111
χ81111111-1-1111-11-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-11111-11-1111-1-1
χ911-11-11111-1-1-1-1111-1-111-1-1111111111-1-1-11-1-1-1-1111-1-1111111-1-1-1-1-1-11-11-111-1-11-11-11-11-11-111-1-111-1-11-11-1
χ1011-11-11111-1-1-1-1111-1-111-1-1111111111-1-1-11-1-1-1-1111-1-1111111-1-1-1-1-1-11-11-1-1-111-11-111-11-11-111-1-1-1-111-11-11
χ1111-11-11111-1-1-1-1111-1-111-1-1111111111-1-1-11-1-1-1-1111-1-1111111-1-1-1-1-1-1-11-1111-1-1-11-11-11-11-11-1-11111-1-1-11-11
χ1211-11-11111-1-1-1-1111-1-111-1-1111111111-1-1-11-1-1-1-1111-1-1111111-1-1-1-1-1-1-11-11-1-1111-11-1-11-11-11-1-111-1-1111-11-1
χ1311-11-111-1-1-1-1-111-1-11111-1-11111-1-1-1-11-1-1-11-1-1-1-111111-1-1-1-1-1-11111111-11-11-1-111-1-111-1-111-1-1-1111-1-111-1-11
χ1411-11-111-1-1-1-1-111-1-11111-1-11111-1-1-1-11-1-1-11-1-1-1-111111-1-1-1-1-1-11111111-11-1-111-1-111-11-1-111-1-1-111-111-1-111-1
χ1511-11-111-1-1-1-1-111-1-11111-1-11111-1-1-1-11-1-1-11-1-1-1-111111-1-1-1-1-1-1111111-11-111-1-11-111-1-111-1-1111-1-11-1-11-111-1
χ1611-11-111-1-1-1-1-111-1-11111-1-11111-1-1-1-11-1-1-11-1-1-1-111111-1-1-1-1-1-1111111-11-11-111-11-1-11-111-1-1111-1-1-111-11-1-11
χ172222222222222222222-122-12-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-1-1-122-1-1-1-122-1-1-1-1222200000000-1-122-1-1-1-1-1-100000000
χ182222222222222222222-122-12-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-20000000011-2-211111100000000
χ19222222222222222222-12-1-12-1222222-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000222200000000000000-1-1-1-1
χ20222222222222222222-12-1-12-1222222-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2000000000000001111
χ212222222-2-2222-22-2-2-2-22-122-12-1-11111-1-1-1-1-1-12-1-12-1-111-2-21111-2-21111222200000000-1-1-2-2-1-1111100000000
χ222222222-2-2222-22-2-2-2-22-122-12-1-11111-1-1-1-1-1-12-1-12-1-111-2-21111-2-21111-2-2-2-200000000112211-1-1-1-100000000
χ232222222-2-2222-22-2-2-2-2-12-1-12-122-2-2-2-2-12-1-1-12-1-1-1-1-1-1-2-21111111111110000000022-2-200000000000000-1-111
χ242222222-2-2222-22-2-2-2-2-12-1-12-122-2-2-2-2-12-1-1-12-1-1-1-1-1-1-2-211111111111100000000-2-2220000000000000011-1-1
χ252222-2-2200-2-220-20000222222-2-2000022222-2-2-2-2-2-2-2000000000000002-2-22000000002-200-22000000000000
χ262222-2-2200-2-220-20000222222-2-2000022222-2-2-2-2-2-2-200000000000000-222-200000000-22002-2000000000000
χ272222-2-2200-2-220-200002-122-121133−3−3-1-1-1-1-11-211-2113−30033−3−30033−3−32-2-2200000000-11001-13−33−300000000
χ282222-2-2200-2-220-200002-122-121133−3−3-1-1-1-1-11-211-2113−30033−3−30033−3−3-222-2000000001-100-11−33−3300000000
χ292222-2-2200-2-220-200002-122-1211−3−333-1-1-1-1-11-211-211−3300−3−33300−3−3332-2-2200000000-11001-1−33−3300000000
χ302222-2-2200-2-220-200002-122-1211−3−333-1-1-1-1-11-211-211−3300−3−33300−3−333-222-2000000001-100-113−33−300000000
χ3122-222-220022-20-2000022-2-222-2-200002-2-2-222222-2-2-20000000000000022-2-2000000002200-2-2000000000000
χ3222-222-220022-20-2000022-2-222-2-200002-2-2-222222-2-2-200000000000000-2-22200000000-2-20022000000000000
χ3322-222-220022-20-200002-1-2-2-121133−3−3-1111-1-12-1-1-211−330033−3−300−3−33322-2-200000000-1-100113−3−3300000000
χ3422-222-220022-20-200002-1-2-2-121133−3−3-1111-1-12-1-1-211−330033−3−300−3−333-2-222000000001100-1-1−333−300000000
χ3522-222-220022-20-200002-1-2-2-1211−3−333-1111-1-12-1-1-2113−300−3−3330033−3−322-2-200000000-1-10011−333−300000000
χ3622-222-220022-20-200002-1-2-2-1211−3−333-1111-1-12-1-1-2113−300−3−3330033−3−3-2-222000000001100-1-13−3−3300000000
χ3722-22-22222-2-2-2-2222-2-22-1-2-2-12-1-1-1-1-1-1-1111-11-2112-1-11122-1-1-1-1-2-211112-22-200000000-112-2-11-1-11100000000
χ3822-22-22222-2-2-2-2222-2-22-1-2-2-12-1-1-1-1-1-1-1111-11-2112-1-11122-1-1-1-1-2-21111-22-22000000001-1-221-111-1-100000000
χ3922-22-22222-2-2-2-2222-2-2-12112-1222222-1-211-1-2111-1-1-1-2-2-1-1-1-1-1-1111111000000002-22-200000000000000-11-11
χ4022-22-22222-2-2-2-2222-2-2-12112-1222222-1-211-1-2111-1-1-1-2-2-1-1-1-1-1-111111100000000-22-22000000000000001-11-1
χ4122-22-222-2-2-2-2-222-2-2222-1-2-2-12-1-11111-1111-11-2112-1-1-1-1-2-2111122-1-1-1-12-22-200000000-11-22-1111-1-100000000
χ4222-22-222-2-2-2-2-222-2-2222-1-2-2-12-1-11111-1111-11-2112-1-1-1-1-2-2111122-1-1-1-1-22-22000000001-12-21-1-1-11100000000
χ4322-22-222-2-2-2-2-222-2-222-12112-122-2-2-2-2-1-211-1-2111-1-1-122111111-1-1-1-1-1-1000000002-2-2200000000000000-111-1
χ4422-22-222-2-2-2-2-222-2-222-12112-122-2-2-2-2-1-211-1-2111-1-1-122111111-1-1-1-1-1-100000000-222-2000000000000001-1-11
χ45444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2111-2-211-211-2-2-2-21111-2-21111000000000000000000000000000000
χ464444444-4-4444-44-4-4-4-4-2-2-2-2-2-2-2-222221-2111-2-211-2112222-1-1-1-122-1-1-1-1000000000000000000000000000000
χ474444-4-4400-4-440-40000-24-2-24-2-4-40000-24-2-2-2-422222200000000000000000000000000000000000000000000
χ484444-4-4400-4-440-40000-2-2-2-2-2-2222323−23−231-211122-1-12-1-123−2300−3−33300−3−333000000000000000000000000000000
χ494444-4-4400-4-440-40000-2-2-2-2-2-222−23−2323231-211122-1-12-1-1−23230033−3−30033−3−3000000000000000000000000000000
χ5044-444-440044-40-40000-24224-2-4-40000-2-422-24-2-2-222200000000000000000000000000000000000000000000
χ5144-444-440044-40-40000-2-222-2-2222323−23−2312-1-11-2-2112-1-1−232300−3−3330033−3−3000000000000000000000000000000
χ5244-444-440044-40-40000-2-222-2-222−23−23232312-1-11-2-2112-1-123−230033−3−300−3−333000000000000000000000000000000
χ5344-44-44444-4-4-4-4444-4-4-2-222-2-2-2-2-2-2-2-212-1-1122-1-1-21122-2-2111122-1-1-1-1000000000000000000000000000000
χ5444-44-444-4-4-4-4-444-4-444-2-222-2-2-2-2222212-1-1122-1-1-211-2-222-1-1-1-1-2-21111000000000000000000000000000000
χ554-40400-422−220000022−22004400-4-40022−2222−224000-400000000022−2222−2222−22000000000000000000000000000000000000
χ564-40400-422−220000022−22004-2002-423−232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23-200020000023−230022−222ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000000000000000
χ574-40400-422−220000022−22004-2002-4−23232ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7-2000200000−23230022−222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000000000000000
χ584-40400-422−220000022−2200-24−2i32i3-420022−2222−22-20−2i32i32000000000−22−22−22i6−i6i6−i6i6−i6000000000000000000000000000000
χ594-40400-422−220000022−2200-242i3−2i3-420022−2222−22-202i3−2i32000000000−22−22−22−i6i6−i6i6−i6i6000000000000000000000000000000
χ604-40400-422−220000022−2200-2-2−2i32i32223−232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2310i3−i3-1003i−3i0−3300−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23000000000000000000000000000000
χ614-40400-422−220000022−2200-2-2−2i32i322−23232ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ710i3−i3-100−3i3i03−300−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23000000000000000000000000000000
χ624-40400-422−220000022−2200-2-22i3−2i32223−232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2310−i3i3-100−3i3i0−3300−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23000000000000000000000000000000
χ634-40400-422−220000022−2200-2-22i3−2i322−23232ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ710−i3i3-1003i−3i03−300−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23000000000000000000000000000000
χ644-40400-4−222200000−2222004400-4-400−2222−22224000-4000000000−2222−2222−2222000000000000000000000000000000000000
χ654-40400-4−222200000−2222004-2002-423−23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23-200020000023−2300−2222−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000000000000000
χ664-40400-4−222200000−2222004-2002-4−2323−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7-2000200000−232300−2222−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000000000000000
χ674-40400-4−222200000−222200-24−2i32i3-4200−2222−2222-20−2i32i320000000002−22−22−2−i6i6−i6i6−i6i6000000000000000000000000000000
χ684-40400-4−222200000−222200-242i3−2i3-4200−2222−2222-202i3−2i320000000002−22−22−2i6−i6i6−i6i6−i6000000000000000000000000000000
χ694-40400-4−222200000−222200-2-2−2i32i32223−23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2310i3−i3-1003i−3i0−33002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23000000000000000000000000000000
χ704-40400-4−222200000−222200-2-2−2i32i322−2323−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ710i3−i3-100−3i3i03−3002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23000000000000000000000000000000
χ714-40400-4−222200000−222200-2-22i3−2i32223−23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2310−i3i3-100−3i3i0−33002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23000000000000000000000000000000
χ724-40400-4−222200000−222200-2-22i3−2i322−2323−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ710−i3i3-1003i−3i03−3002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23000000000000000000000000000000
χ73666-366-366-3-3-36-3-3-3-3-3000000000000000000000000000000000000000000222200000000000000-1-1-1-10000
χ74666-366-366-3-3-36-3-3-3-3-3000000000000000000000000000000000000000000-2-2-2-20000000000000011110000
χ75666-366-3-6-6-3-3-3-6-333330000000000000000000000000000000000000000002-22-200000000000000-11-110000
χ76666-366-3-6-6-3-3-3-6-33333000000000000000000000000000000000000000000-22-22000000000000001-11-10000
χ7766-6-3-66-366333-6-3-3-33300000000000000000000000000000000000000000022-2-200000000000000-1-1110000
χ7866-6-3-66-366333-6-3-3-333000000000000000000000000000000000000000000-2-2220000000000000011-1-10000
χ7966-6-3-66-3-6-63336-333-3-30000000000000000000000000000000000000000002-2-2200000000000000-111-10000
χ8066-6-3-66-3-6-63336-333-3-3000000000000000000000000000000000000000000-222-2000000000000001-1-110000
χ81121212-6-12-12-60066-606000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-612-12-600-6-6606000000000000000000000000000000000000000000000000000000000000000000000000
χ8312-120-600662−6263−63000−323236−3600000000000000000000000000000000000000000000000000000000000000000000
χ8412-120-600662−62−6363000−3232−363600000000000000000000000000000000000000000000000000000000000000000000
χ8512-120-6006−626263−6300032−32−363600000000000000000000000000000000000000000000000000000000000000000000
χ8612-120-6006−6262−636300032−3236−3600000000000000000000000000000000000000000000000000000000000000000000

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