Finite Group Databasebeta

← Group #13155946

Character table — Group #13155946

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112222222222244444444444444444444888888888888881212242424242424242424242424242424242424242424242424242436363636363636367272727272108108
order1223334466612123336666661212121212121212121212366666612121212121212246666881212121224242424242424242424242424242424224412121212466121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-111-1-1
χ411111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-111
χ511111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-111-1-1-1-1
χ611111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111
χ711111111111111111111111111111111111111111111111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-111
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ9222222-2-2222-2-2222222222-2-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-200000000000000000000000000002-200000002-20000
χ10222222-2-2222-2-2222222222-2-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-20000000000000000000000000000-220000000-220000
χ1122222-122-12222-1-122-1-1-1222222-1-12-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-100000022000022-1-1-1-1-1-122-1-1-1-1-1-1220000000-1-10000
χ1222222-122-12222-1-122-1-1-1222222-1-12-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-10000002-2000022-1-1-1-1-1-1-2-2111111-2-20000000110000
χ1322222-122-12222-1-122-1-1-1222222-1-12-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-1000000-220000-2-211111122-1-1-1-1-1-1-2-20000000110000
χ1422222-122-12222-1-122-1-1-1222222-1-12-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-1000000-2-20000-2-2111111-2-2111111220000000-1-10000
χ1522222-1-2-2-122-2-2-1-122-1-1-122-2-2-2-211-21111-1-1-12-1-1-111-2111100000000000000333−3−3−300333−3−3−32-20000000-110000
χ1622222-1-2-2-122-2-2-1-122-1-1-122-2-2-2-211-21111-1-1-12-1-1-111-2111100000000000000333−3−3−300−3−3−3333-2200000001-10000
χ1722222-1-2-2-122-2-2-1-122-1-1-122-2-2-2-211-21111-1-1-12-1-1-111-2111100000000000000−3−3−333300333−3−3−3-2200000001-10000
χ1822222-1-2-2-122-2-2-1-122-1-1-122-2-2-2-211-21111-1-1-12-1-1-111-2111100000000000000−3−3−333300−3−3−33332-20000000-110000
χ192222-122222-1222-1-1-122-1-122-1-1-122-122-1-1-12-1-1-1-1-12-1-1-1-1-1-1222-1-1-1022-1-1-100000000-1-12-1-12-1-100000000200-1-100
χ202222-122222-1222-1-1-122-1-122-1-1-122-122-1-1-12-1-1-1-1-12-1-1-1-1-1-1222-1-1-10-22-1-1-10000000011-211-21100000000-2001100
χ212222-122222-1222-1-1-122-1-122-1-1-122-122-1-1-12-1-1-1-1-12-1-1-1-1-1-1-2-2-211102-211100000000-1-12-1-12-1-100000000-2001100
χ222222-122222-1222-1-1-122-1-122-1-1-122-122-1-1-12-1-1-1-1-12-1-1-1-1-1-1-2-2-21110-2-21110000000011-211-21100000000200-1-100
χ23222-122222-12-1-1-12-122-12-1-1-12-1-1222-1-122-1-12-1-1-1-1-12-1-1-1-1-122-12-1-120-12-1-1-1-12-1-12-1-1000000000022-1-1-1-10000000
χ24222-122222-12-1-1-12-122-12-1-1-12-1-1222-1-122-1-12-1-1-1-1-12-1-1-1-1-122-12-1-1-20-12-1-111-211-2110000000000-2-211110000000
χ25222-122222-12-1-1-12-122-12-1-1-12-1-1222-1-122-1-12-1-1-1-1-12-1-1-1-1-1-2-21-211201-211-1-12-1-12-1-10000000000-2-211110000000
χ26222-122222-12-1-1-12-122-12-1-1-12-1-1222-1-122-1-12-1-1-1-1-12-1-1-1-1-1-2-21-211-201-21111-211-211000000000022-1-1-1-10000000
χ2722-22222-222222222-2-2222-2-22222-2-222-2-22-2-2-2-2-22-22-222-2-2000000000000000000000000000000000000000002-2
χ2822-22222-222222222-2-2222-2-22222-2-222-2-22-2-2-2-2-22-22-222-2-200000000000000000000000000000000000000000-22
χ2922-2222-22222-2-2222-2-2222-22-2-2-2-222-2-2222-2-2-2-2-222-22-2-2222-2222200-2-2-2-20000000000000000000000000000000
χ3022-2222-22222-2-2222-2-2222-22-2-2-2-222-2-2222-2-2-2-2-222-22-2-222-22-2-2-2-20022220000000000000000000000000000000
χ3122-22-12-2222-1-2-22-1-11-22-1-1-22111-22-1-2-2-1-1-1-21111-121-111-1-12-22-1-1-100-211100000000−i3i30−i3i30−i3i300000000000−i3i300
χ3222-22-12-2222-1-2-22-1-11-22-1-1-22111-22-1-2-2-1-1-1-21111-121-111-1-12-22-1-1-100-211100000000i3−i30i3−i30i3−i300000000000i3−i300
χ3322-22-12-2222-1-2-22-1-11-22-1-1-22111-22-1-2-2-1-1-1-21111-121-111-1-1-22-2111002-1-1-100000000−i3i30−i3i30−i3i300000000000i3−i300
χ3422-22-12-2222-1-2-22-1-11-22-1-1-22111-22-1-2-2-1-1-1-21111-121-111-1-1-22-2111002-1-1-100000000i3−i30i3−i30i3−i300000000000−i3i300
χ3522-2-122-222-1211-12-1-2-2-12-11-1-211-2221122-11-2111-1-1-2-111-1-12-2-12-1-1001-2113−303−303−300000000000033−3−30000000
χ3622-2-122-222-1211-12-1-2-2-12-11-1-211-2221122-11-2111-1-1-2-111-1-12-2-12-1-1001-211−330−330−33000000000000−3−3330000000
χ3722-2-122-222-1211-12-1-2-2-12-11-1-211-2221122-11-2111-1-1-2-111-1-1-221-21100-12-1-13−303−303−3000000000000−3−3330000000
χ3822-2-122-222-1211-12-1-2-2-12-11-1-211-2221122-11-2111-1-1-2-111-1-1-221-21100-12-1-1−330−330−3300000000000033−3−30000000
χ394444-24-4-444-2-4-44-2-2-244-2-24-4222-4-42-4-422-24-2-2-2-2-2-42222220000000000000000000000000000000000000000000
χ404444-2-244-24-244-21-2-2-2-21-244-2-2-2-2-2-2-2-2111-21-2111-21-2111100000004000000000000-2-2-211-211000000000000000
χ414444-2-244-24-244-21-2-2-2-21-244-2-2-2-2-2-2-2-2111-21-2111-21-211110000000-4000000000000222-1-12-1-1000000000000000
χ424444-2-2-4-4-24-2-4-4-21-2-2-2-21-24-422222222-1-11-21-21112-12-1-1-1-1000000000000000000000023−3−3−2333000000000000000
χ434444-2-2-4-4-24-2-4-4-21-2-2-2-21-24-422222222-1-11-21-21112-12-1-1-1-10000000000000000000000−233323−3−3000000000000000
χ44444-244-4-44-2422-24-244-24-2-22-422-4-4-422-4-4-2-24-2-2-2-22-4222220000000000000000000000000000000000000000000
χ45444-24-244-2-24-2-21-2-24-21-2-2-2-24-2-2-2-2411-2-211-2-21111-2-21111000000400000-2-2-211-21100000000000000000000000
χ46444-24-244-2-24-2-21-2-24-21-2-2-2-24-2-2-2-2411-2-211-2-21111-2-21111000000-400000222-1-12-1-100000000000000000000000
χ47444-24-2-4-4-2-24221-2-24-21-2-2-22-42222-4-1-12211-2-2111-122-1-1-1-10000000000000023−3−3−233300000000000000000000000
χ48444-24-2-4-4-2-24221-2-24-21-2-2-22-42222-4-1-12211-2-2111-122-1-1-1-100000000000000−233323−3−300000000000000000000000
χ49444-2-24444-2-2-2-2-2-21-24-2-21-2-2-21144-2-2-2-2-21-2-21111-2-21111144-2-21100-2-2110000000000000000000000000000000
χ50444-2-24444-2-2-2-2-2-21-24-2-21-2-2-21144-2-2-2-2-21-2-21111-2-211111-4-422-1-10022-1-10000000000000000000000000000000
χ51444-2-24-4-44-2-222-2-21-24-2-21-222-1-1-4-4222221-2-2111122-1-1-1-1-100003-300003-30000000000000000000000000000000
χ52444-2-24-4-44-2-222-2-21-24-2-21-222-1-1-4-4222221-2-2111122-1-1-1-1-10000-330000-330000000000000000000000000000000
χ5344-444-24-4-24444-2-24-42-2-24-4-4444-22-4-2-222-222-422-22-2-4-2-2220000000000000000000000000000000000000000000
χ5444-444-2-44-244-4-4-2-24-42-2-24-44-4-4-42-2422-2-2-222-422-2-22422-2-20000000000000000000000000000000000000000000
χ5544-44-244-444-2444-2-22-44-2-2-4-4-2-2-24-424422-2-42222-2-4-22-2-2220000000000000000000000000000000000000000000
χ5644-44-2-24-4-24-244-21-222-21-2-4-4-2-2-2-222-2-2-1-112-12-1-1121211-1-1000000000000000000000003i−3i0−3i3i000000000000000
χ5744-44-2-24-4-24-244-21-222-21-2-4-4-2-2-2-222-2-2-1-112-12-1-1121211-1-100000000000000000000000−3i3i03i−3i000000000000000
χ5844-44-2-2-44-24-2-4-4-21-222-21-2-442222-2-2221112-12-1-11-2-1-2-1-11100000000000000000000−2i32i30i3−i30i3−i3000000000000000
χ5944-44-2-2-44-24-2-4-4-21-222-21-2-442222-2-2221112-12-1-11-2-1-2-1-111000000000000000000002i3−2i30−i3i30−i3i3000000000000000
χ6044-4-2444-44-24-2-2-24-2-4-4-24-2224-2-24-4-4-2-2-4-4-22-4222-2242-2-2220000000000000000000000000000000000000000000
χ6144-4-24-24-4-2-24-2-21-2-2-421-2-2224-2-2-22-411221-122-1-11-1-2211-1-10000000000000003-30-3300000000000000000000000
χ6244-4-24-24-4-2-24-2-21-2-2-421-2-2224-2-2-22-411221-122-1-11-1-2211-1-1000000000000000-3303-300000000000000000000000
χ6344-4-24-2-44-2-24221-2-2-421-2-22-2-4222-24-1-1-2-21-122-1-1112-2-1-11100000000000023−230−330−3300000000000000000000000
χ6444-4-24-2-44-2-24221-2-2-421-2-22-2-4222-24-1-1-2-21-122-1-1112-2-1-111000000000000−232303−303−300000000000000000000000
χ6544-4-2-244-44-2-2-2-2-2-212-4-2-2122-2114-42-2-222122-1-1-112-2-111-1-100003-30000-330000000000000000000000000000000
χ6644-4-2-244-44-2-2-2-2-2-212-4-2-2122-2114-42-2-222122-1-1-112-2-111-1-10000-3300003-30000000000000000000000000000000
χ6744-4-2-24-444-2-222-2-212-4-2-212-22-1-1-44-222-2-2122-1-1-11-221-1-1114-4-2-2110022-1-10000000000000000000000000000000
χ6844-4-2-24-444-2-222-2-212-4-2-212-22-1-1-44-222-2-2122-1-1-11-221-1-111-4422-1-100-2-2110000000000000000000000000000000
χ694-4044400-4-4-40044400-4-4-4000000000000400000-400000000000000000000000000000000000002i−2i2i−2i2i−2i0000000
χ704-4044400-4-4-40044400-4-4-4000000000000400000-40000000000000000000000000000000000000−2i2i−2i2i−2i2i0000000
χ714-40-24400-42-423−23-24-2002-4200023−2300023−2300-200000200023−23000000000000000000000000000000002i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000
χ724-40-24400-42-423−23-24-2002-4200023−2300023−2300-200000200023−2300000000000000000000000000000000−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000
χ734-40-24400-42-4−2323-24-2002-42000−2323000−232300-2000002000−2323000000000000000000000000000000002i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000
χ744-40-24400-42-4−2323-24-2002-42000−2323000−232300-2000002000−232300000000000000000000000000000000−2i2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000
χ75888-4-4-488-4-4-4-4-4222-4-4222-4-4-422-4-4-42222-1222-1-1-1222-1-1-1-10000000000000000000000000000000000000000000
χ76888-4-4-4-8-8-4-4-444222-4-4222-444-2-2444-2-2-2-2-1222-1-1-1-2-2-211110000000000000000000000000000000000000000000
χ7788-8-4-4-48-8-4-4-4-4-42224422244-422-44422-2-2-1-2-2-211-1-22-2-1-1110000000000000000000000000000000000000000000
χ7888-8-4-4-4-88-4-4-444222442224-44-2-24-4-4-2-222-1-2-2-211-12-2211-1-10000000000000000000000000000000000000000000
χ798-8088-4004-8-800-4-480044-8000000000000-400000400000000000000000000000000000000000000000000000000
χ808-808-4800-8-84008-4-400-844000000000000-400000400000000000000000000000000000000000000000000000000
χ818-808-4-4004-8400-42-4004-2400000000006i−6i200000-2000006i−6i0000000000000000000000000000000000000000000
χ828-808-4-4004-8400-42-4004-240000000000−6i6i200000-200000−6i6i0000000000000000000000000000000000000000000
χ838-80-48-40044-843−432-4-400-24400043−43000−232300200000-2000−2323000000000000000000000000000000000000000000000
χ848-80-48-40044-8−43432-4-400-244000−434300023−2300200000-200023−23000000000000000000000000000000000000000000000
χ858-80-4-4800-84443−43-4-420044-2000−232300043−4300200000-2000−2323000000000000000000000000000000000000000000000
χ868-80-4-4800-844−4343-4-420044-200023−23000−434300200000-200023−23000000000000000000000000000000000000000000000
χ878-80-4-4-40044443−4322200-2-2-2000−2323000−23236i−6i-1000−3i33i310003−3−3i3i0000000000000000000000000000000000000000000
χ888-80-4-4-40044443−4322200-2-2-2000−2323000−2323−6i6i-10003i3−3i310003−33i−3i0000000000000000000000000000000000000000000
χ898-80-4-4-400444−434322200-2-2-200023−2300023−236i−6i-10003i3−3i31000−33−3i3i0000000000000000000000000000000000000000000
χ908-80-4-4-400444−434322200-2-2-200023−2300023−23−6i6i-1000−3i33i31000−333i−3i0000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.