Finite Group Databasebeta

← Group #13139022

Character table — Group #13139022

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size112222222222222444446666666612121212121212121212121212121212121212121212121212121212363636363636363636363636727272727272727272727272
order12234468812122424242468122424336666121236666121212121212122424242424242424242424242424242424668812122424242444881212121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111-1-111-1-1-1-11-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-11-111-1-111-1-1
χ61111111-1-111-1-1-1-11-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-11-11-1-111-1-111
χ71111111-1-111-1-1-1-11-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1111-1-1-1-111
χ81111111-1-111-1-1-1-11-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-111-1-1-11111-1-1
χ9222222222222222222222-122-12-1-1-1-1-1-1-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000220000-1-1-1-1
χ10222222222222222222222-122-12-1-1-1-1-1-1-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000-2-200001111
χ1122222222222222222222-12-1-12-122-12-1-1-1-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000002200-1-1-1-10000
χ1222222222222222222222-12-1-12-122-12-1-1-1-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000-2-20011110000
χ132222222-2-222-2-2-2-22-22-2-22-122-12-1-1-1-1-1-1-12-1-1-12-1-1-2-2-2-2111111111111000000000000002-20000-1-111
χ142222222-2-222-2-2-2-22-22-2-22-122-12-1-1-1-1-1-1-12-1-1-12-1-1-2-2-2-211111111111100000000000000-22000011-1-1
χ152222222-2-222-2-2-2-22-22-2-2-12-1-12-122-12-1-1-1-1-1-12-1-1-11111-2-2-2-2111111110000000000002-200-1-1110000
χ162222222-2-222-2-2-2-22-22-2-2-12-1-12-122-12-1-1-1-1-1-12-1-1-11111-2-2-2-211111111000000000000-220011-1-10000
χ172222-2-2200-2-2000020-200222222-2-222222-2-2-2-2-2-2-2000000000000000000002i−2i002i2i−2i−2i000000000000
χ182222-2-2200-2-2000020-200222222-2-222222-2-2-2-2-2-2-200000000000000000000−2i2i00−2i−2i2i2i000000000000
χ1922-222-2222222222-2-2-2-2-222-2-222-2-22-2-2-22-2-2-2222222-2-222-2-22222-2-2-2-2000000000000000000000000
χ2022-222-2222222222-2-2-2-2-22-1-2-2-1211-1111-1-211-12-1-122-2-2-1-111-1-1-1-11111000000000000000000003−33−3
χ2122-222-2222222222-2-2-2-2-22-1-2-2-1211-1111-1-211-12-1-122-2-2-1-111-1-1-1-1111100000000000000000000−33−33
χ2222-222-2222222222-2-2-2-2-2-12112-1-2-2-1-211-11112-1-1-1-1-11122-2-2-1-1-1-111110000000000000000−i3i3−i3i30000
χ2322-222-2222222222-2-2-2-2-2-12112-1-2-2-1-211-11112-1-1-1-1-11122-2-2-1-1-1-111110000000000000000i3−i3i3−i30000
χ2422-222-22-2-222-2-2-2-2-22-22222-2-222-2-22-2-2-22-2-2-22222-2-222-2-222-2-2-2-22222000000000000000000000000
χ2522-222-22-2-222-2-2-2-2-22-2222-1-2-2-1211-1111-1-211-12-1-1-2-22211-1-11111-1-1-1-1000000000000000000003−3−33
χ2622-222-22-2-222-2-2-2-2-22-2222-1-2-2-1211-1111-1-211-12-1-1-2-22211-1-11111-1-1-1-100000000000000000000−333−3
χ2722-222-22-2-222-2-2-2-2-22-222-12112-1-2-2-1-211-11112-1-1-111-1-1-2-2221111-1-1-1-10000000000000000−i3i3i3−i30000
χ2822-222-22-2-222-2-2-2-2-22-222-12112-1-2-2-1-211-11112-1-1-111-1-1-2-2221111-1-1-1-10000000000000000i3−i3−i3i30000
χ2922-22-22200-2-20000-2020022-2-222222-2-2-22222-2-2-2-200000000000000002-22200-2-20000000000000000
χ3022-22-22200-2-20000-2020022-2-222222-2-2-22222-2-2-2-20000000000000000-22-2-200220000000000000000
χ3144444444444444444444-2-2-2-2-2-2-2-21-2111-211-2-211-2-2-2-2-2-2-2-211111111000000000000000000000000
χ324444444-4-444-4-4-4-44-44-4-4-2-2-2-2-2-2-2-21-2111-211-2-21122222222-1-1-1-1-1-1-1-1000000000000000000000000
χ334444-4-4400-4-4000040-4004-244-2422-2-2-2-2-2-4222-4220000000000000000000000000000000000000000
χ344444-4-4400-4-4000040-400-24-2-24-2-4-4-24-2-2-2222-42220000000000000000000000000000000000000000
χ354444-4-4400-4-4000040-400-2-2-2-2-2-2221-21112-1-122-1-1000000003i3i−3i−3i3i3i−3i−3i000000000000000000000000
χ364444-4-4400-4-4000040-400-2-2-2-2-2-2221-21112-1-122-1-100000000−3i−3i3i3i−3i−3i3i3i000000000000000000000000
χ3744-444-4444444444-4-4-4-4-4-2-222-2-22212-1-112-1-1-2-211-2-222-2-2221111-1-1-1-1000000000000000000000000
χ3844-444-44-4-444-4-4-4-4-44-444-2-222-2-22212-1-112-1-1-2-21122-2-222-2-2-1-1-1-11111000000000000000000000000
χ3944-44-44400-4-40000-404004-2-4-4-24-2-2-2222-24-2-22-4220000000000000000000000000000000000000000
χ4044-44-44400-4-40000-40400-24224-244-2-422-2-2-2-2-42220000000000000000000000000000000000000000
χ4144-44-44400-4-40000-40400-2-222-2-2-2-212-1-11-21122-1-1000000003i3i−3i−3i−3i−3i3i3i000000000000000000000000
χ4244-44-44400-4-40000-40400-2-222-2-2-2-212-1-11-21122-1-100000000−3i−3i3i3i3i3i−3i−3i000000000000000000000000
χ434-40400-422−22002222−22−22000004400-4-4004000-4000000022−220022−220022−2222−220000000000000000000000000000
χ444-40400-422−22002222−22−22000004-2002-423−23-20002023−23000022−2200−226−6−22−226−66−6000000000000000000000000
χ454-40400-422−22002222−22−22000004-2002-4−2323-200020−2323000022−2200−22−66−22−22−66−66000000000000000000000000
χ464-40400-422−22002222−22−2200000-24−2i32i3-4200-20−2i32i320000000−22i6−i622−2200−22−22i6−i6−i6i6000000000000000000000000
χ474-40400-422−22002222−22−2200000-242i3−2i3-4200-202i3−2i320000000−22−i6i622−2200−22−22−i6i6i6−i6000000000000000000000000
χ484-40400-422−22002222−22−2200000-2-2−2i32i32223−2310i3−i3-10−33003i−3i−22i6−i6−226−6ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ494-40400-422−22002222−22−2200000-2-2−2i32i322−232310i3−i3-103−300−3i3i−22i6−i6−22−66−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ504-40400-422−22002222−22−2200000-2-22i3−2i32223−2310−i3i3-10−3300−3i3i−22−i6i6−226−6−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ514-40400-422−22002222−22−2200000-2-22i3−2i322−232310−i3i3-103−3003i−3i−22−i6i6−22−66ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ524-40400-4−222200−22−222222000004400-4-4004000-40000000−222200−222200−2222−22220000000000000000000000000000
χ534-40400-4−222200−22−222222000004-2002-423−23-20002023−230000−2222002−2−662−22−2−66−66000000000000000000000000
χ544-40400-4−222200−22−222222000004-2002-4−2323-200020−23230000−2222002−26−62−22−26−66−6000000000000000000000000
χ554-40400-4−222200−22−22222200000-24−2i32i3-4200-20−2i32i3200000002−2−i6i6−2222002−22−2−i6i6i6−i6000000000000000000000000
χ564-40400-4−222200−22−22222200000-242i3−2i3-4200-202i3−2i3200000002−2i6−i6−2222002−22−2i6−i6−i6i6000000000000000000000000
χ574-40400-4−222200−22−22222200000-2-2−2i32i32223−2310i3−i3-10−33003i−3i2−2−i6i62−2−66−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ584-40400-4−222200−22−22222200000-2-2−2i32i322−232310i3−i3-103−300−3i3i2−2−i6i62−26−62ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ594-40400-4−222200−22−22222200000-2-22i3−2i32223−2310−i3i3-10−3300−3i3i2−2i6−i62−2−662ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ604-40400-4−222200−22−22222200000-2-22i3−2i322−232310−i3i3-103−3003i−3i2−2i6−i62−26−6−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ61666-366-366-3-3-3-3-3-3-36-3-3-300000000000000000000000000000000000022-1-122-1-1-1-1-1-1000000000000
χ62666-366-366-3-3-3-3-3-3-36-3-3-3000000000000000000000000000000000000-2-211-2-2111111000000000000
χ63666-366-3-6-6-3-33333-3-6-33300000000000000000000000000000000000022-1-1-2-2-1-11111000000000000
χ64666-366-3-6-6-3-33333-3-6-333000000000000000000000000000000000000-2-2112211-1-1-1-1000000000000
χ65666-3-6-6-3003333−3333−33-30333−3300000000000000000000000000000000000000−i3i32i−2i−i3i3−i−iii000000000000
χ66666-3-6-6-3003333−3333−33-30333−3300000000000000000000000000000000000000i3−i3−2i2ii3−i3ii−i−i000000000000
χ67666-3-6-6-30033−3333−3333-303−333300000000000000000000000000000000000000−i3i3−2i2i−i3i3ii−i−i000000000000
χ68666-3-6-6-30033−3333−3333-303−333300000000000000000000000000000000000000i3−i32i−2ii3−i3−i−iii000000000000
χ6966-6-36-6-366-3-3-3-3-3-33-633300000000000000000000000000000000000000−i3i300i3−i3−i3i3−i3i3000000000000
χ7066-6-36-6-366-3-3-3-3-3-33-633300000000000000000000000000000000000000i3−i300−i3i3i3−i3i3−i3000000000000
χ7166-6-36-6-3-6-6-3-33333363-3-300000000000000000000000000000000000000−i3i300i3−i3i3−i3i3−i3000000000000
χ7266-6-36-6-3-6-6-3-33333363-3-300000000000000000000000000000000000000i3−i300−i3i3−i3i3−i3i3000000000000
χ7366-6-3-66-3003333−3333−3330-3−33330000000000000000000000000000000000002-2-1-100113−3−33000000000000
χ7466-6-3-66-3003333−3333−3330-3−3333000000000000000000000000000000000000-221100-1-1−333−3000000000000
χ7566-6-3-66-30033−3333−333330-333−330000000000000000000000000000000000002-2-1-10011−333−3000000000000
χ7666-6-3-66-30033−3333−333330-333−33000000000000000000000000000000000000-221100-1-13−3−33000000000000
χ7712-120-600662−6263−636ζ5−6ζ76ζ13−6ζ23−6ζ5+6ζ7−6ζ13+6ζ2300000000000000000000000000000000000000000000000000000000000000000
χ7812-120-600662−62−63636ζ13−6ζ236ζ5−6ζ7−6ζ13+6ζ23−6ζ5+6ζ700000000000000000000000000000000000000000000000000000000000000000
χ7912-120-6006−626263−63−6ζ5+6ζ7−6ζ13+6ζ236ζ5−6ζ76ζ13−6ζ2300000000000000000000000000000000000000000000000000000000000000000
χ8012-120-6006−6262−6363−6ζ13+6ζ23−6ζ5+6ζ76ζ13−6ζ236ζ5−6ζ700000000000000000000000000000000000000000000000000000000000000000

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