Finite Group Databasebeta

← Group #13138722

Character table — Group #13138722

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size112222222222222444446666666612121212121212121212121212121212121212121212121212121212363636363636363636363636727272727272727272727272
order12234468812122424242468122424336666121236666121212121212122424242424242424242424242424242416161616484848484848484822246666661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511-11-11111111111-1-1-1-1-111-1-111-1-11-1-1-11-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-11-11111-1-1-1-1
χ611-11-11111111111-1-1-1-1-111-1-111-1-11-1-1-11-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-11-1-1-1-11111
χ711-11-11111111111-1-1-1-1-111-1-111-1-11-1-1-11-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-11-1-111-1-111
χ811-11-11111111111-1-1-1-1-111-1-111-1-11-1-1-11-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-111-1-111-1-1
χ9222222222222222222222-1-1-1-1222-12-1-1-1-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000220000-1-1-1-100
χ10222222222222222222222-1-1-1-1222-12-1-1-1-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000-2-20000111100
χ1122222222222222222222-12222-1-1-1-1-1-1-1-12-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000000000000022-1-10000-1-1
χ1222222222222222222222-12222-1-1-1-1-1-1-1-12-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100000000000000-2-211000011
χ132222222-2-222-2-2-2-22-22-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ142222222-2-222-2-2-2-22-22-2-22-1-1-1-1222-12-1-1-1-1-1-1-12-1-1-2-2111111-2-2111111000000000000000000−i3i3−i3i300
χ152222222-2-222-2-2-2-22-22-2-22-1-1-1-1222-12-1-1-1-1-1-1-12-1-1-2-2111111-2-2111111000000000000000000i3−i3i3−i300
χ162222222-2-222-2-2-2-22-22-2-2-12222-1-1-1-1-1-1-1-12-1-12-1-1-111-2-2111111-2-211110000000000000000−i3i30000−i3i3
χ172222222-2-222-2-2-2-22-22-2-2-12222-1-1-1-1-1-1-1-12-1-12-1-1-111-2-2111111-2-211110000000000000000i3−i30000i3−i3
χ182222-2-2200-2-2000020-200222222-2-222222-2-2-2-2-2-2-200000000000000002−22−222−2−222−2−2000000000000
χ192222-2-2200-2-2000020-200222222-2-222222-2-2-2-2-2-2-20000000000000000−22−22−2−222−2−222000000000000
χ2022-222-2200-2-20000-2020022-2-222222-2-2-22222-2-2-2-200000000000000002−2−2222−2−2−2−222000000000000
χ2122-222-2200-2-20000-2020022-2-222222-2-2-22222-2-2-2-20000000000000000−222−2−2−22222−2−2000000000000
χ2222-22-22222222222-2-2-2-2-22-111-12-2-2-1-211-1111-12-1-122-1-1-1-1-1-1-2-21111110000000000002-20000-1-11100
χ2322-22-22222222222-2-2-2-2-22-111-12-2-2-1-211-1111-12-1-122-1-1-1-1-1-1-2-2111111000000000000-22000011-1-100
χ2422-22-22222222222-2-2-2-2-2-12-2-22-111-1111-1-2112-1-1-1-1-122-1-1-1-111-2-21111000000000000002-2-1-1000011
χ2522-22-22222222222-2-2-2-2-2-12-2-22-111-1111-1-2112-1-1-1-1-122-1-1-1-111-2-2111100000000000000-22110000-1-1
χ2622-22-222-2-222-2-2-2-2-22-22222-2-222-2-22-2-2-22-2-2-22222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ2722-22-222-2-222-2-2-2-2-22-2222-111-12-2-2-1-211-1111-12-1-1-2-211111122-1-1-1-1-1-1000000000000000000−i3i3i3−i300
χ2822-22-222-2-222-2-2-2-2-22-2222-111-12-2-2-1-211-1111-12-1-1-2-211111122-1-1-1-1-1-1000000000000000000i3−i3−i3i300
χ2922-22-222-2-222-2-2-2-2-22-222-12-2-22-111-1111-1-2112-1-1-111-2-21111-1-122-1-1-1-10000000000000000−i3i30000i3−i3
χ3022-22-222-2-222-2-2-2-2-22-222-12-2-22-111-1111-1-2112-1-1-111-2-21111-1-122-1-1-1-10000000000000000i3−i30000−i3i3
χ3144444444444444444444-2-2-2-2-2-2-2-21-2111-211-2-211-2-2-2-21111-2-2-2-21111000000000000000000000000
χ324444444-4-444-4-4-4-44-44-4-4-2-2-2-2-2-2-2-21-2111-211-2-2112222-1-1-1-12222-1-1-1-1000000000000000000000000
χ334444-4-4400-4-4000040-4004-2-2-2-24-4-4-24-2-2-22222-4220000000000000000000000000000000000000000
χ344444-4-4400-4-4000040-400-24444-222-2-2-2-2-2-422-42220000000000000000000000000000000000000000
χ354444-4-4400-4-4000040-400-2-2-2-2-2-2221-21112-1-122-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000
χ364444-4-4400-4-4000040-400-2-2-2-2-2-2221-21112-1-122-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000
χ3744-444-4400-4-40000-404004-222-2444-2-422-2-2-2-22-4220000000000000000000000000000000000000000
χ3844-444-4400-4-40000-40400-24-4-44-2-2-2-2222-24-2-2-42220000000000000000000000000000000000000000
χ3944-444-4400-4-40000-40400-2-222-2-2-2-212-1-11-21122-1-100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000000
χ4044-444-4400-4-40000-40400-2-222-2-2-2-212-1-11-21122-1-10000−3i−3i3i3i00003i3i−3i−3i000000000000000000000000
χ4144-44-44444444444-4-4-4-4-4-2-222-2-22212-1-112-1-1-2-211-2-2-2-211112222-1-1-1-1000000000000000000000000
χ4244-44-444-4-444-4-4-4-4-44-444-2-222-2-22212-1-112-1-1-2-2112222-1-1-1-1-2-2-2-21111000000000000000000000000
χ434-40400-422−22002222−22−22000004400-4-4004000-4000000022−2222−2222−2222−2200000000000000000000000000000000
χ444-40400-422−22002222−22−22000004-2−2i32i32-400-20−2i32i32000000022−22−22−22−2200i6−i6i6−i6i6−i6000000000000000000000000
χ454-40400-422−22002222−22−22000004-22i3−2i32-400-202i3−2i32000000022−22−22−22−2200−i6i6−i6i6−i6i6000000000000000000000000
χ464-40400-422−22002222−22−2200000-2400-4223−23-20002023−230000−2222−22−22−226−6006−6−66000000000000000000000000
χ474-40400-422−22002222−22−2200000-2400-42−2323-200020−23230000−2222−22−22−22−6600−666−6000000000000000000000000
χ484-40400-422−22002222−22−2200000-2-2−2i32i32223−2310i3−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−ζ23000000000000000000000000
χ494-40400-422−22002222−22−2200000-2-2−2i32i322−232310i3−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−ζ13000000000000000000000000
χ504-40400-422−22002222−22−2200000-2-22i3−2i32223−2310−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+ζ13000000000000000000000000
χ514-40400-422−22002222−22−2200000-2-22i3−2i322−232310−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+ζ23000000000000000000000000
χ524-40400-4−222200−22−222222000004400-4-4004000-40000000−2222−2222−2222−222200000000000000000000000000000000
χ534-40400-4−222200−22−222222000004-2−2i32i32-400-20−2i32i320000000−22222−22−22−200−i6i6−i6i6−i6i6000000000000000000000000
χ544-40400-4−222200−22−222222000004-22i3−2i32-400-202i3−2i320000000−22222−22−22−200i6−i6i6−i6i6−i6000000000000000000000000
χ554-40400-4−222200−22−22222200000-2400-4223−23-20002023−2300002−2−22222−22−2−6600−666−6000000000000000000000000
χ564-40400-4−222200−22−22222200000-2400-42−2323-200020−232300002−2−22222−22−26−6006−6−66000000000000000000000000
χ574-40400-4−222200−22−22222200000-2-2−2i32i32223−2310i3−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+ζ23000000000000000000000000
χ584-40400-4−222200−22−22222200000-2-2−2i32i322−232310i3−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+ζ13000000000000000000000000
χ594-40400-4−222200−22−22222200000-2-22i3−2i32223−2310−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−ζ13000000000000000000000000
χ604-40400-4−222200−22−22222200000-2-22i3−2i322−232310−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−ζ23000000000000000000000000
χ61666-366-366-3-3-3-3-3-3-36-3-3-30000000000000000000000000000000000002222-1-1-1-1-1-1-1-1000000000000
χ62666-366-366-3-3-3-3-3-3-36-3-3-3000000000000000000000000000000000000-2-2-2-211111111000000000000
χ63666-366-3-6-6-3-33333-3-6-33300000000000000000000000000000000000000003−33−33−33−3000000000000
χ64666-366-3-6-6-3-33333-3-6-3330000000000000000000000000000000000000000−33−33−33−33000000000000
χ65666-3-6-6-3003333−3333−33-30333−330000000000000000000000000000000000002−22−2ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ66666-3-6-6-3003333−3333−33-30333−33000000000000000000000000000000000000−22−22−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000
χ67666-3-6-6-30033−3333−3333-303−33330000000000000000000000000000000000002−22−2ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ68666-3-6-6-30033−3333−3333-303−3333000000000000000000000000000000000000−22−22−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000
χ6966-6-36-6-3003333−3333−3330-3−33330000000000000000000000000000000000002−2−22ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23000000000000
χ7066-6-36-6-3003333−3333−3330-3−3333000000000000000000000000000000000000−222−2−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23000000000000
χ7166-6-36-6-30033−3333−333330-333−330000000000000000000000000000000000002−2−22ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7000000000000
χ7266-6-36-6-30033−3333−333330-333−33000000000000000000000000000000000000−222−2−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7000000000000
χ7366-6-3-66-366-3-3-3-3-3-33-633300000000000000000000000000000000000022-2-2-1-1-1-11111000000000000
χ7466-6-3-66-366-3-3-3-3-3-33-6333000000000000000000000000000000000000-2-2221111-1-1-1-1000000000000
χ7566-6-3-66-3-6-6-3-33333363-3-300000000000000000000000000000000000000003−33−3−33−33000000000000
χ7666-6-3-66-3-6-6-3-33333363-3-30000000000000000000000000000000000000000−33−333−33−3000000000000
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.