Finite Group Databasebeta

← Group #13168422

Character table — Group #13168422

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121244443666121212121212121212121212244466121212121212121212121212121244121212126661212121212121212121212121244444121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-111-1-1-111-1-11111111111111111-1-1-111-11111-1-111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-11111111111-1-111-1-1-1-1-1-1-1-1-1-1111-11111-1-11111-1-1-1-1-111-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-11-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-1-111-1-1-1-1-1-111-1111
χ51111111111111111111111111111111-1-111111111111111111111-1111-1-111-1-111-1-11111-1-1-1-1-1-11111-11-1-11111-1-111-111-1-1-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111-1-1-111-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-111-1-1-1-11111111111111-1-1-1-1-111-1-111-1-1-11-11-1-1-1-1-1111-11-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-11111111111-1-1-1-1-11-1-1111111-1-1-1-11-11-1-111-1-1-11-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-111-111-1-1-1-111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111111111-1-11111111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-11-11111-1-1-1-1-1-111-1-11111111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-111-111-1-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-11111-1-1-1-111111111111-111-1-1-1-1-1-111-1-11-11-1-111-1-1-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1111111-1-1-111111-1-111-1-111-11-11-1-1-1-1-1111-1-11
χ17222222-122-1-1222-122-1-122-1-1-12-1-12-1222200-1-1-1-12-1-1-122-1-1-1-1-1-1202222-1-1-1-12200220000000000-1-1-10-12-1-100-1-1-1-1000002200-1-100-1000
χ18222222-122-1-1222-122-1-122-1-1-12-1-12-1222200-1-1-1-12-1-1-122-1-1-1-1-1-1-202-2-2-2-1-11122002200000000001110-1-2-1-10011-1-100000-2-20011001000
χ19222222-122-1-1222-122-1-122-1-1-12-1-12-122-2-200-1-1-1-12-1-1-122-1-1-1-1-1-120-222211-1-1-2-200-2-20000000000-1-1-10121100-1-11100000-2-20011001000
χ20222222-122-1-1222-122-1-122-1-1-12-1-12-122-2-200-1-1-1-12-1-1-122-1-1-1-1-1-1-20-2-2-2-21111-2-200-2-2000000000011101-211001111000002200-1-100-1000
χ21222222-122-1-1222-122-1-1-22-1-1-12-1-12-1-2-22200-1-1-1-1-2111-2-211111120-2-222-1-1112200-2-20000000000-1-1-101-2110011-1-1000002-2001100-1000
χ22222222-122-1-1222-122-1-1-22-1-1-12-1-12-1-2-22200-1-1-1-1-2111-2-2111111-20-22-2-2-1-1-1-12200-2-200000000001110121100-1-1-1-100000-2200-1-1001000
χ23222222-122-1-1222-122-1-1-22-1-1-12-1-12-1-2-2-2-200-1-1-1-1-2111-2-2111111202-2221111-2-200220000000000-1-1-10-1-2-1-100111100000-2200-1-1001000
χ24222222-122-1-1222-122-1-1-22-1-1-12-1-12-1-2-2-2-200-1-1-1-1-2111-2-2111111-2022-2-211-1-1-2-2002200000000001110-12-1-100-1-111000002-2001100-1000
χ2522222-12-1-1222222-1-12-12-12-1-1-12-1-12220022-1-1-1-1-12-1-1-1-122-1-1-1-12202-1-1002200220022-1-10000002-1-1-10-100-1-1-1-100-1-1022000000-1-10-100
χ2622222-12-1-1222222-1-12-12-12-1-1-12-1-12220022-1-1-1-1-12-1-1-1-122-1-1-1-1-220-21100-2-200220022-1-1000000-211-10100-1-11100-1-10-2-2000000110100
χ2722222-12-1-1222222-1-12-12-12-1-1-12-1-122200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-12-202-1-1002200-2-200-2-2110000002-1-110-10011-1-100110-2-2000000110100
χ2822222-12-1-1222222-1-12-12-12-1-1-12-1-122200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2-20-21100-2-200-2-200-2-211000000-2111010011110011022000000-1-10-100
χ2922222-12-1-1222222-1-12-1-2-12-1-1-12-1-12-2-20022-1-1-1-11-21111-2-211112-20-2-1-100-2-200-2-20022-1-10000002-1-110100-1-111001102-2000000-1-10100
χ3022222-12-1-1222222-1-12-1-2-12-1-1-12-1-12-2-20022-1-1-1-11-21111-2-21111-2-20211002200-2-20022-1-1000000-21110-100-1-1-1-100110-22000000110-100
χ3122222-12-1-1222222-1-12-1-2-12-1-1-12-1-12-2-200-2-2-1-1-1-11-21111-2-21111220-2-1-100-2-2002200-2-2110000002-1-1-10100111100-1-10-22000000110-100
χ3222222-12-1-1222222-1-12-1-2-12-1-1-12-1-12-2-200-2-2-1-1-1-11-21111-2-21111-2202110022002200-2-211000000-211-10-10011-1-100-1-102-2000000-1-10100
χ332222-1222222-1-1-122-1-122-1-122-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-10220002200-1-1-1-1-1-1-1-12222-1-1-1-1000220-1-1-1-100-1-1-1-120000-1-100000000
χ342222-1222222-1-1-122-1-122-1-122-1-12-1-1-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-220002200-1-111-1-111-2-2-2-21111000-220-1-11100-1-111-200001100000000
χ352222-1222222-1-1-122-1-122-1-122-1-12-1-1-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-102-2000-2-20011-1-111-1-122-2-211110002-2011-1-10011-1-1-200001100000000
χ362222-1222222-1-1-122-1-122-1-122-1-12-1-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-2-2000-2-20011111111-2-222-1-1-1-1000-2-20111100111120000-1-100000000
χ372222-1222222-1-1-122-1-12-2-1-122-1-12-1-1112222-1-1-1-1-2-2-2-2111111110-2-20002200-1-11111-1-12222-1-1-1-1000-2-2011-1-100-1-111-200001100000000
χ382222-1222222-1-1-122-1-12-2-1-122-1-12-1-11122-2-2-1-1-1-1-2-2-2-21111111102-20002200-1-1-1-11111-2-2-2-211110002-20111100-1-1-1-120000-1-100000000
χ392222-1222222-1-1-122-1-12-2-1-122-1-12-1-111-2-222-1-1-1-1-2-2-2-2111111110-22000-2-2001111-1-1-1-122-2-21111000-220-1-1-1-100111120000-1-100000000
χ402222-1222222-1-1-122-1-12-2-1-122-1-12-1-111-2-2-2-2-1-1-1-1-2-2-2-211111111022000-2-20011-1-1-1-111-2-222-1-1-1-1000220-1-1110011-1-1-200001100000000
χ412-22-2222-2-2-22-2-22-222220-2-2-2-2222-2-2002i−2i2-222-2-20000000000000000002i−2i002i−2i00002-22-22i−2i2i2i−2i−2i000000002-2002i−2i00000000000000000
χ422-22-2222-2-2-22-2-22-222220-2-2-2-2222-2-2002i−2i-2222-2-20000000000000000002i−2i002i−2i0000-22-22−2i2i−2i−2i2i2i00000000-22002i−2i00000000000000000
χ432-22-2222-2-2-22-2-22-222220-2-2-2-2222-2-200−2i2i2-222-2-2000000000000000000−2i2i00−2i2i00002-22-2−2i2i−2i−2i2i2i000000002-200−2i2i00000000000000000
χ442-22-2222-2-2-22-2-22-222220-2-2-2-2222-2-200−2i2i-2222-2-2000000000000000000−2i2i00−2i2i0000-22-222i−2i2i2i−2i−2i00000000-2200−2i2i00000000000000000
χ452-22-2-122-2-2-2211-1-22-1-12011-2-2-1-12113−32i−2i2-2-1-11100003−33−333−3−30000002i−2i00−ii3−3−i3i3-112-22i−2i−i−iii000000−i3i3-1100−ii3−300000−i3i300000000
χ462-22-2-122-2-2-2211-1-22-1-12011-2-2-1-12113−32i−2i-22-1-11100003−33−333−3−30000002i−2i00−ii−33−i3i31-1-22−2i2iii−i−i000000−i3i31-100−ii−3300000i3−i300000000
χ472-22-2-122-2-2-2211-1-22-1-12011-2-2-1-12113−3−2i2i2-2-1-11100003−33−333−3−3000000−2i2i00i−i3−3i3−i3-112-2−2i2iii−i−i000000i3−i3-1100i−i3−300000i3−i300000000
χ482-22-2-122-2-2-2211-1-22-1-12011-2-2-1-12113−3−2i2i-22-1-11100003−33−333−3−3000000−2i2i00i−i−33i3−i31-1-222i−2i−i−iii000000i3−i31-100i−i−3300000−i3i300000000
χ492-22-2-122-2-2-2211-1-22-1-12011-2-2-1-1211−332i−2i2-2-1-1110000−33−33−3−3330000002i−2i00−ii−33i3−i3-112-22i−2i−i−iii000000i3−i3-1100−ii−3300000i3−i300000000
χ502-22-2-122-2-2-2211-1-22-1-12011-2-2-1-1211−332i−2i-22-1-1110000−33−33−3−3330000002i−2i00−ii3−3i3−i31-1-22−2i2iii−i−i000000i3−i31-100−ii3−300000−i3i300000000
χ512-22-2-122-2-2-2211-1-22-1-12011-2-2-1-1211−33−2i2i2-2-1-1110000−33−33−3−333000000−2i2i00i−i−33−i3i3-112-2−2i2iii−i−i000000−i3i3-1100i−i−3300000−i3i300000000
χ522-22-2-122-2-2-2211-1-22-1-12011-2-2-1-1211−33−2i2i-22-1-1110000−33−33−3−333000000−2i2i00i−i3−3−i3i31-1-222i−2i−i−iii000000−i3i31-100i−i3−300000i3−i300000000
χ5344444-2-2-2-2-2-2444-2-2-2-214-2-211-2-21-2-24400001111-2-211-2-2-2-211114004-2-200-2-20000000000000000-21100-20000110000000000000000000
χ5444444-2-2-2-2-2-2444-2-2-2-214-2-211-2-21-2-24400001111-2-211-2-2-2-21111-400-422002200000000000000002-1-10020000-1-10000000000000000000
χ5544444-2-2-2-2-2-2444-2-2-2-21-4-2-211-2-21-2-2-4-40000111122-1-12222-1-1-1-1400-4-2-200220000000000000000-2110020000-1-10000000000000000000
χ5644444-2-2-2-2-2-2444-2-2-2-21-4-2-211-2-21-2-2-4-40000111122-1-12222-1-1-1-1-40042200-2-200000000000000002-1-100-20000110000000000000000000
χ574444-24-244-2-2-2-2-2-24-21-24-21-2-2-21-2-21-2-2440011114-2-2-2-2-2111111004000-2-200-2-200-2-200000000000000-201100001100000000000000000
χ584444-24-244-2-2-2-2-2-24-21-24-21-2-2-21-2-21-2-2-4-40011114-2-2-2-2-211111100-400022002200220000000000000020-1-10000-1-100000000000000000
χ594444-24-244-2-2-2-2-2-24-21-2-4-21-2-2-21-2-212244001111-422222-1-1-1-1-1-100-4000-2-200-2-200220000000000000020-1-100001100000000000000000
χ604444-24-244-2-2-2-2-2-24-21-2-4-21-2-2-21-2-2122-4-4001111-422222-1-1-1-1-1-100400022002200-2-200000000000000-20110000-1-100000000000000000
χ614444-2-24-2-244-2-2-24-21-2-241-2-2-21-2-21-2-2-200441111-24-2-211-2-21111040000000000-2-200-2-2-2-2000000000-2000011000011000000000000000
χ624444-2-24-2-244-2-2-24-21-2-241-2-2-21-2-21-2-2-200-4-41111-24-2-211-2-211110-400000000002200222200000000020000-1-10000-1-1000000000000000
χ634444-2-24-2-244-2-2-24-21-2-2-41-2-2-21-2-21-222004411112-422-1-122-1-1-1-10-400000000002200-2-2-2-200000000020000110000-1-1000000000000000
χ644444-2-24-2-244-2-2-24-21-2-2-41-2-2-21-2-21-22200-4-411112-422-1-122-1-1-1-1040000000000-2-2002222000000000-20000-1-1000011000000000000000
χ6544-4-4444-444-44-4-4-4-44440-4-4-44-4-4-4440000004-4-44000000000000000000000000000000000000000000000000000000000000000000000
χ6644-4-444-2-44-224-4-42-44-2-20-422-2-4224-2000000-222-2000000000000000000000000000000000000000000000000000000000000023−23000000
χ6744-4-444-2-44-224-4-42-44-2-20-422-2-4224-2000000-222-20000000000000000000000000000000000000000000000000000000000000−2323000000
χ6844-4-44-242-24-44-4-4-42-24-202-42-22-42-24000000-222-200000000000000000000000000000000000000000000000000000000000000023−230000
χ6944-4-44-242-24-44-4-4-42-24-202-42-22-42-24000000-222-2000000000000000000000000000000000000000000000000000000000000000−23230000
χ7044-4-4-244-444-4-222-4-4-2-24022-4422-4-2-2000000-222-2000000000000000000000000000000000023−2323−230000000000000000000000000000000
χ7144-4-4-244-444-4-222-4-4-2-24022-4422-4-2-2000000-222-20000000000000000000000000000000000−2323−23230000000000000000000000000000000
χ724-44-444-2-4-42-2-4-44244-2-20-42224-2-2-42004i−4i00-2-222000000000000000000−2i2i004i−4i00000000000000000000000000−2i2i00000000000000000
χ734-44-444-2-4-42-2-4-44244-2-20-42224-2-2-4200−4i4i00-2-2220000000000000000002i−2i00−4i4i000000000000000000000000002i−2i00000000000000000
χ744-44-44-2422-44-4-44-4-2-24-202-422-24-22-400004-4-2-22200000000000000000000000000004-4-2200000000000000-22000000000000000000000
χ754-44-44-2422-44-4-44-4-2-24-202-422-24-22-40000-44-2-2220000000000000000000000000000-442-2000000000000002-2000000000000000000000
χ764-44-4-24-2-4-42-222-224-21-202-122-21-22-123−234i−4i0011-1-1000023−23−33−3−333000000−2i2i00−2i2i00−2i32i30000000000000000i3−i30000i−i00000000000000000
χ774-44-4-24-2-4-42-222-224-21-202-122-21-22-123−23−4i4i0011-1-1000023−23−33−3−3330000002i−2i002i−2i002i3−2i30000000000000000−i3i30000−ii00000000000000000
χ784-44-4-24-2-4-42-222-224-21-202-122-21-22-1−23234i−4i0011-1-10000−23233−333−3−3000000−2i2i00−2i2i002i3−2i30000000000000000−i3i30000i−i00000000000000000
χ794-44-4-24-2-4-42-222-224-21-202-122-21-22-1−2323−4i4i0011-1-10000−23233−333−3−30000002i−2i002i−2i00−2i32i30000000000000000i3−i30000−ii00000000000000000
χ804-44-4-2-2422-4422-2-4-21-2-20-12221-2-2-1223−23004-411-1-10000−3323−23−3−33300000000000023−2300-22-22000000000000001-10000−33000000000000000
χ814-44-4-2-2422-4422-2-4-21-2-20-12221-2-2-1223−2300-4411-1-10000−3323−23−3−333000000000000−2323002-22-200000000000000-1100003−3000000000000000
χ824-44-4-2-2422-4422-2-4-21-2-20-12221-2-2-12−2323004-411-1-100003−3−232333−3−3000000000000−232300-22-22000000000000001-100003−3000000000000000
χ834-44-4-2-2422-4422-2-4-21-2-20-12221-2-2-12−232300-4411-1-100003−3−232333−3−300000000000023−23002-22-200000000000000-110000−33000000000000000
χ844-4-444444-4-4-4-44-44-44440444-4-4-4-4-4-40000004-44-4000000000000000000000000000000000000000000000000000000000000000000000
χ854-4-4444-24-422-44-4-2-44-2-204-2-22-422-42000000-22-220000000000000000000023−230000000000000000000000000023−230000000000000000000
χ864-4-4444-24-422-44-4-2-44-2-204-2-22-422-42000000-22-2200000000000000000000−232300000000000000000000000000−23230000000000000000000
χ874-4-444-24-22-4-4-44-442-24-20-24-222-422-4000000-22-220000000000000000−2i32i3000000000000000000000−2i32i30000000000000000000000000000
χ884-4-444-24-22-4-4-44-442-24-20-24-222-422-4000000-22-2200000000000000002i3−2i30000000000000000000002i3−2i30000000000000000000000000000
χ894-4-444-2-2-2222-44-4-22-2-210-2-21-122-1220000001-11-1003i−3i00003i−3i3i−3i0000−2i32i30023−2300000000000000000i3−i30000000−330000000000000000000
χ904-4-444-2-2-2222-44-4-22-2-210-2-21-122-1220000001-11-1003i−3i00003i−3i3i−3i00002i3−2i300−232300000000000000000−i3i300000003−30000000000000000000
χ914-4-444-2-2-2222-44-4-22-2-210-2-21-122-1220000001-11-100−3i3i0000−3i3i−3i3i0000−2i32i300−232300000000000000000i3−i300000003−30000000000000000000
χ924-4-444-2-2-2222-44-4-22-2-210-2-21-122-1220000001-11-100−3i3i0000−3i3i−3i3i00002i3−2i30023−2300000000000000000−i3i30000000−330000000000000000000
χ934-4-44-2444-4-4-42-224-4-2-240-2-24-422-422000000-22-220000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ944-4-44-2444-4-4-42-224-4-2-240-2-24-422-422000000-22-2200000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-44-4-448-8-844-4-42044-2244-2-4-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-4-88-44-4444-8-42-404-24-44-24-420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-484-48-8-444-842-4-40-244-4-2442-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-44-4-44-444442220-2-2-22-2-2-222000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-44-4-44-444442220-2-2-22-2-2-222000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000
χ1028-88-88-4-4444-4-8-884-4-4-42044-2-2-4-424400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-4444-444-44-42220-2-2-2-2222-2-243−430000-1-1110000−2323−232333−3−3000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-4444-444-44-42220-2-2-2-2222-2-2−43430000-1-111000023−2323−23−3−333000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-48-8444-44-4-8-42-40-42-444-244-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48-44-8-84-44842-4-402-4-44-244-240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4-44444-44-442220222-2-2-2-2-2-2000000-11-11006i−6i0000−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-44444-44-442220222-2-2-2-2-2-2000000-11-1100−6i6i00003i−3i3i−3i000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).