Finite Group Databasebeta

← Group #13149816

Character table — Group #13149816

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size112222222222222444446666666612121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order12234468812122424242468122424336666121236666121212121212122424242424242424242424242424242422442222224466881212242424246666661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ51111111-1-111-1-1-1-11-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-11-111-1-111-1-1-1-11-111-1-11-1
χ61111111-1-111-1-1-1-11-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-1111-1-111-1-1-1-1-11-1-111-11
χ71111111-1-111-1-1-1-11-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-11-1-111-1-11111-1111-1-1-11
χ81111111-1-111-1-1-1-11-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-111-1-111111-1-1-1111-1
χ911-11-11111111111-1-1-1-1-111-1-111-1-11-1-1-11-1-1-1111111111111-1-1-1-1-1-1-1-11-11-11-11-111-1-11-11-11-111-1-1111-11-1-1-1
χ1011-11-11111111111-1-1-1-1-111-1-111-1-11-1-1-11-1-1-1111111111111-1-1-1-1-1-1-1-11-11-1-11-11-1-1111-11-11-111-1-1-1-1-11-1111
χ1111-11-11111111111-1-1-1-1-111-1-111-1-11-1-1-11-1-1-1111111111111-1-1-1-1-1-1-1-1-11-111-11-1-1-111-11-11-11-1-111-1-11-11-111
χ1211-11-11111111111-1-1-1-1-111-1-111-1-11-1-1-11-1-1-1111111111111-1-1-1-1-1-1-1-1-11-11-11-1111-1-1-11-11-11-1-11111-11-11-1-1
χ1311-11-111-1-111-1-1-1-1-11-11111-1-111-1-11-1-1-11-1-1-11111-1-1-1-1-1-1-1-1111111111-11-11-1-111-1-111-1-111-1-1-1111-11-1-11-11
χ1411-11-111-1-111-1-1-1-1-11-11111-1-111-1-11-1-1-11-1-1-11111-1-1-1-1-1-1-1-1111111111-11-1-111-1-111-11-1-111-1-1-111-11-111-11-1
χ1511-11-111-1-111-1-1-1-1-11-11111-1-111-1-11-1-1-11-1-1-11111-1-1-1-1-1-1-1-111111111-11-111-1-11-111-1-111-1-1111-1-1-111-1-111-1
χ1611-11-111-1-111-1-1-1-1-11-11111-1-111-1-11-1-1-11-1-1-11111-1-1-1-1-1-1-1-111111111-11-11-111-11-1-11-111-1-1111-1-11-1-111-1-11
χ17222222222222222222222-1-1-1-1222-12-1-1-1-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1000022220000000000000000-1-1-1-100
χ18222222222222222222222-1-1-1-1222-12-1-1-1-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-10000-2-2-2-20000000000000000111100
χ1922222222222222222222-12222-1-1-1-1-1-1-1-12-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000000022220000000000-1-10000-1-1
χ2022222222222222222222-12222-1-1-1-1-1-1-1-12-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100000000-2-2-2-2000000000011000011
χ212222222-2-222-2-2-2-22-22-2-22-1-1-1-1222-12-1-1-1-1-1-1-12-1-1-2-2111111-2-2111111000022-2-20000000000000000-1-11100
χ222222222-2-222-2-2-2-22-22-2-22-1-1-1-1222-12-1-1-1-1-1-1-12-1-1-2-2111111-2-21111110000-2-222000000000000000011-1-100
χ232222222-2-222-2-2-2-22-22-2-2-12222-1-1-1-1-1-1-1-12-1-12-1-1-111-2-2111111-2-21111000000002-22-20000000000-110000-11
χ242222222-2-222-2-2-2-22-22-2-2-12222-1-1-1-1-1-1-1-12-1-12-1-1-111-2-2111111-2-2111100000000-22-2200000000001-100001-1
χ252222-2-2200-2-2000020-200222222-2-222222-2-2-2-2-2-2-200000000000000002-2-22000000002-200-22000000000000
χ262222-2-2200-2-2000020-200222222-2-222222-2-2-2-2-2-2-20000000000000000-222-200000000-22002-2000000000000
χ2722-222-2200-2-20000-2020022-2-222222-2-2-22222-2-2-2-2000000000000000022-2-2000000002200-2-2000000000000
χ2822-222-2200-2-20000-2020022-2-222222-2-2-22222-2-2-2-20000000000000000-2-22200000000-2-20022000000000000
χ2922-22-22222222222-2-2-2-2-22-111-12-2-2-1-211-1111-12-1-122-1-1-1-1-1-1-2-211111100002-22-20000000000000000-11-1100
χ3022-22-22222222222-2-2-2-2-22-111-12-2-2-1-211-1111-12-1-122-1-1-1-1-1-1-2-21111110000-22-2200000000000000001-11-100
χ3122-22-22222222222-2-2-2-2-2-12-2-22-111-1111-1-2112-1-1-1-1-122-1-1-1-111-2-211110000000022-2-20000000000-1-1000011
χ3222-22-22222222222-2-2-2-2-2-12-2-22-111-1111-1-2112-1-1-1-1-122-1-1-1-111-2-2111100000000-2-2220000000000110000-1-1
χ3322-22-222-2-222-2-2-2-2-22-2222-111-12-2-2-1-211-1111-12-1-1-2-211111122-1-1-1-1-1-100002-2-220000000000000000-111-100
χ3422-22-222-2-222-2-2-2-2-22-2222-111-12-2-2-1-211-1111-12-1-1-2-211111122-1-1-1-1-1-10000-222-200000000000000001-1-1100
χ3522-22-222-2-222-2-2-2-2-22-222-12-2-22-111-1111-1-2112-1-1-111-2-21111-1-122-1-1-1-1000000002-2-220000000000-1100001-1
χ3622-22-222-2-222-2-2-2-2-22-222-12-2-22-111-1111-1-2112-1-1-111-2-21111-1-122-1-1-1-100000000-222-200000000001-10000-11
χ3744444444444444444444-2-2-2-2-2-2-2-21-2111-211-2-211-2-2-2-21111-2-2-2-21111000000000000000000000000000000
χ384444444-4-444-4-4-4-44-44-4-4-2-2-2-2-2-2-2-21-2111-211-2-2112222-1-1-1-12222-1-1-1-1000000000000000000000000000000
χ394444-4-4400-4-4000040-4004-2-2-2-24-4-4-24-2-2-22222-4220000000000000000000000000000000000000000000000
χ404444-4-4400-4-4000040-400-24444-222-2-2-2-2-2-422-42220000000000000000000000000000000000000000000000
χ414444-4-4400-4-4000040-400-2-2-2-2-2-2221-21112-1-122-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000
χ424444-4-4400-4-4000040-400-2-2-2-2-2-2221-21112-1-122-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000000
χ4344-444-4400-4-40000-404004-222-2444-2-422-2-2-2-22-4220000000000000000000000000000000000000000000000
χ4444-444-4400-4-40000-40400-24-4-44-2-2-2-2222-24-2-2-42220000000000000000000000000000000000000000000000
χ4544-444-4400-4-40000-40400-2-222-2-2-2-212-1-11-21122-1-100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000000
χ4644-444-4400-4-40000-40400-2-222-2-2-2-212-1-11-21122-1-10000−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000000
χ4744-44-44444444444-4-4-4-4-4-2-222-2-22212-1-112-1-1-2-211-2-2-2-211112222-1-1-1-1000000000000000000000000000000
χ4844-44-444-4-444-4-4-4-4-44-444-2-222-2-22212-1-112-1-1-2-2112222-1-1-1-1-2-2-2-21111000000000000000000000000000000
χ494-40400-422−22002222−22−22000004400-4-4004000-4000000022−2222−2222−2222−2200000000000000000000000000000000000000
χ504-40400-422−22002222−22−22000004-2−2i32i32-400-20−2i32i32000000022−22−22−22−2200i6−i6i6−i6i6−i6000000000000000000000000000000
χ514-40400-422−22002222−22−22000004-22i3−2i32-400-202i3−2i32000000022−22−22−22−2200−i6i6−i6i6−i6i6000000000000000000000000000000
χ524-40400-422−22002222−22−2200000-2400-4223−23-20002023−230000−2222−22−22−226−6006−6−66000000000000000000000000000000
χ534-40400-422−22002222−22−2200000-2400-42−2323-200020−23230000−2222−22−22−22−6600−666−6000000000000000000000000000000
χ544-40400-422−22002222−22−2200000-2-2−2i32i32223−2310i3−i3-10−33003i−3i−22−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ554-40400-422−22002222−22−2200000-2-2−2i32i322−232310i3−i3-103−300−3i3i−22−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ564-40400-422−22002222−22−2200000-2-22i3−2i32223−2310−i3i3-10−3300−3i3i−22−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ236−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ574-40400-422−22002222−22−2200000-2-22i3−2i322−232310−i3i3-103−3003i−3i−22−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ584-40400-4−222200−22−222222000004400-4-4004000-40000000−2222−2222−2222−222200000000000000000000000000000000000000
χ594-40400-4−222200−22−222222000004-2−2i32i32-400-20−2i32i320000000−22222−22−22−200−i6i6−i6i6−i6i6000000000000000000000000000000
χ604-40400-4−222200−22−222222000004-22i3−2i32-400-202i3−2i320000000−22222−22−22−200i6−i6i6−i6i6−i6000000000000000000000000000000
χ614-40400-4−222200−22−22222200000-2400-4223−23-20002023−2300002−2−22222−22−2−6600−666−6000000000000000000000000000000
χ624-40400-4−222200−22−22222200000-2400-42−2323-200020−232300002−2−22222−22−26−6006−6−66000000000000000000000000000000
χ634-40400-4−222200−22−22222200000-2-2−2i32i32223−2310i3−i3-10−33003i−3i2−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ644-40400-4−222200−22−22222200000-2-2−2i32i322−232310i3−i3-103−300−3i3i2−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ236−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ654-40400-4−222200−22−22222200000-2-22i3−2i32223−2310−i3i3-10−3300−3i3i2−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ664-40400-4−222200−22−22222200000-2-22i3−2i322−232310−i3i3-103−3003i−3i2−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ67666-366-366-3-3-3-3-3-3-36-3-3-3000000000000000000000000000000000000222200000000-1-122-1-1-1-1-1-100000000
χ68666-366-366-3-3-3-3-3-3-36-3-3-3000000000000000000000000000000000000-2-2-2-20000000011-2-211111100000000
χ69666-366-3-6-6-3-33333-3-6-333000000000000000000000000000000000000222200000000-1-1-2-2-1-1111100000000
χ70666-366-3-6-6-3-33333-3-6-333000000000000000000000000000000000000-2-2-2-200000000112211-1-1-1-100000000
χ71666-3-6-6-3003333−3333−33-30333−330000000000000000000000000000000000002-2-2200000000-11001-13−33−300000000
χ72666-3-6-6-3003333−3333−33-30333−33000000000000000000000000000000000000-222-2000000001-100-11−33−3300000000
χ73666-3-6-6-30033−3333−3333-303−33330000000000000000000000000000000000002-2-2200000000-11001-1−33−3300000000
χ74666-3-6-6-30033−3333−3333-303−3333000000000000000000000000000000000000-222-2000000001-100-113−33−300000000
χ7566-6-36-6-3003333−3333−3330-3−333300000000000000000000000000000000000022-2-200000000-1-100113−3−3300000000
χ7666-6-36-6-3003333−3333−3330-3−3333000000000000000000000000000000000000-2-222000000001100-1-1−333−300000000
χ7766-6-36-6-30033−3333−333330-333−3300000000000000000000000000000000000022-2-200000000-1-10011−333−300000000
χ7866-6-36-6-30033−3333−333330-333−33000000000000000000000000000000000000-2-222000000001100-1-13−3−3300000000
χ7966-6-3-66-366-3-3-3-3-3-33-63330000000000000000000000000000000000002-22-200000000-112-2-11-1-11100000000
χ8066-6-3-66-366-3-3-3-3-3-33-6333000000000000000000000000000000000000-22-22000000001-1-221-111-1-100000000
χ8166-6-3-66-3-6-6-3-33333363-3-30000000000000000000000000000000000002-22-200000000-11-22-1111-1-100000000
χ8266-6-3-66-3-6-6-3-33333363-3-3000000000000000000000000000000000000-22-22000000001-12-21-1-1-11100000000
χ8312-120-600662−6263−636ζ5−6ζ76ζ13−6ζ23−6ζ5+6ζ7−6ζ13+6ζ2300000000000000000000000000000000000000000000000000000000000000000000000
χ8412-120-600662−62−63636ζ13−6ζ236ζ5−6ζ7−6ζ13+6ζ23−6ζ5+6ζ700000000000000000000000000000000000000000000000000000000000000000000000
χ8512-120-6006−626263−63−6ζ5+6ζ7−6ζ13+6ζ236ζ5−6ζ76ζ13−6ζ2300000000000000000000000000000000000000000000000000000000000000000000000
χ8612-120-6006−6262−6363−6ζ13+6ζ23−6ζ5+6ζ76ζ13−6ζ236ζ5−6ζ700000000000000000000000000000000000000000000000000000000000000000000000

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