Finite Group Databasebeta

← Group #13167033

Character table — Group #13167033

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122224444444444444444444888888888888888818181818242424242424242424242424242424242424363636363636363672727272108108108108
order12223666333346666666666661212366612121212121212121212121244444412121212121212121212121212121212444412121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1
χ6111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ7111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1-1-1-1-111111111-1-111-1-1-1-111-1-111
χ8111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1-1-1-1-1111111-1-11111-1-111-1-111-1-1
χ92222222222222222222222222222222222222222222-2-2-2-20000000000000000000000-2-2-2-200000000
χ10222222222222-2222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222-2-20000000000000000000000-2-22200000000
χ112222-1-1-1-122-1-1222-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1222222-1-1-1-122-1-1-1-122-1-1-1-10000-1-1-1-100000000
χ122222-1-1-1-122-1-1222-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-2-21111-2-21111-2-211110000-1-1-1-100000000
χ132222-1-1-1-122-1-1222-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-200−i3i3−i3i300−i3−i3i3i300−i3−i3i3i30000111100000000
χ142222-1-1-1-122-1-1222-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-200i3−i3i3−i300i3i3−i3−i300i3i3−i3−i30000111100000000
χ152222-1-1-1-122-1-1-222-1-12-1-12-1-12211-1-1-1-1-2-21111-2-2111122-2-200−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3000011-1-100000000
χ162222-1-1-1-122-1-1-222-1-12-1-12-1-12211-1-1-1-1-2-21111-2-2111122-2-200i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3000011-1-100000000
χ172222-1-1-1-122-1-1-222-1-12-1-12-1-12211-1-1-1-1-2-21111-2-21111-2-2222-2-1-11122-1-1-1-1-2-211110000-1-11100000000
χ182222-1-1-1-122-1-1-222-1-12-1-12-1-12211-1-1-1-1-2-21111-2-21111-2-222-2211-1-1-2-2111122-1-1-1-10000-1-11100000000
χ192-22-22-2-22222202-2-2-2-2-2-2222-2-20022-2-20000000000002-2000000000000000000000000002-20000−i2i2−i2i2
χ202-22-22-2-22222202-2-2-2-2-2-2222-2-20022-2-20000000000002-2000000000000000000000000002-20000i2−i2i2−i2
χ212-22-22-2-22222202-2-2-2-2-2-2222-2-20022-2-2000000000000-2200000000000000000000000000-220000−i2i2i2−i2
χ222-22-22-2-22222202-2-2-2-2-2-2222-2-20022-2-2000000000000-2200000000000000000000000000-220000i2−i2−i2i2
χ232-2-222-22-222220-2222-2-2-2-2-2-22-2002-22-2000000000000002-2000000000000000000002-22-2002-2000000
χ242-2-222-22-222220-2222-2-2-2-2-2-22-2002-22-2000000000000002-200000000000000000000-222-200-22000000
χ252-2-222-22-222220-2222-2-2-2-2-2-22-2002-22-200000000000000-220000000000000000002i−2i00-2200002i−2i0000
χ262-2-222-22-222220-2222-2-2-2-2-2-22-2002-22-200000000000000-22000000000000000000−2i2i00-220000−2i2i0000
χ27444444441-2114-2111111111-2-244-2-2-2-2111111-2-2-2-2-2-20000222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ28444444441-2114-2111111111-2-244-2-2-2-2111111-2-2-2-2-2-20000-2-2-2-2-2-21111111111110000000000000000
χ29444444441-211-4-2111111111-2-2-4-4-2-2-2-2-1-1-1-1-1-122222200002-222-2-2-1-1-1-1-1-11111110000000000000000
χ30444444441-211-4-2111111111-2-2-4-4-2-2-2-2-1-1-1-1-1-12222220000-22-2-222111111-1-1-1-1-1-10000000000000000
χ3144444444-21-2-241-2-2-2-2-2-2-2-2-211441111-2-2-2-2-2-2111111000000000000000000000022220000-1-1-1-10000
χ3244444444-21-2-241-2-2-2-2-2-2-2-2-211441111-2-2-2-2-2-21111110000000000000000000000-2-2-2-2000011110000
χ3344444444-21-2-2-41-2-2-2-2-2-2-2-2-211-4-41111222222-1-1-1-1-1-1000000000000000000000022-2-2000011-1-10000
χ3444444444-21-2-2-41-2-2-2-2-2-2-2-2-211-4-41111222222-1-1-1-1-1-10000000000000000000000-2-2220000-1-1110000
χ354444-2-2-2-21-2−1−3i32−1+3i324-21−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-21111000022−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i320000000000000000
χ364444-2-2-2-21-2−1−3i32−1+3i324-21−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-211110000-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i320000000000000000
χ374444-2-2-2-21-2−1−3i32−1+3i32-4-21−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2221111-1-11+3i321+3i321−3i321−3i3222-1-1-1-100002-2−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i320000000000000000
χ384444-2-2-2-21-2−1−3i32−1+3i32-4-21−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2221111-1-11+3i321+3i321−3i321−3i3222-1-1-1-10000-221+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i320000000000000000
χ394444-2-2-2-21-2−1+3i32−1−3i324-21−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-21111000022−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i320000000000000000
χ404444-2-2-2-21-2−1+3i32−1−3i324-21−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-211110000-2-21−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i320000000000000000
χ414444-2-2-2-21-2−1+3i32−1−3i32-4-21−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2221111-1-11−3i321−3i321+3i321+3i3222-1-1-1-100002-2−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i320000000000000000
χ424444-2-2-2-21-2−1+3i32−1−3i32-4-21−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2221111-1-11−3i321−3i321+3i321+3i3222-1-1-1-10000-221−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i320000000000000000
χ4344-4-444-4-41-21102-1-1-1111-1-1-12-200-222-23-33-33-300000000000000003−33−33−33−33−33−30000000000000000
χ4444-4-444-4-41-21102-1-1-1111-1-1-12-200-222-23-33-33-30000000000000000−33−33−33−33−33−330000000000000000
χ4544-4-444-4-41-21102-1-1-1111-1-1-12-200-222-2-33-33-3300000000000000003−33−33−3−33−33−330000000000000000
χ4644-4-444-4-41-21102-1-1-1111-1-1-12-200-222-2-33-33-330000000000000000−33−33−333−33−33−30000000000000000
χ4744-4-444-4-444440-4-4-4-4444-4-4-4-44004-4-4400000000000000000000000000000000000000000000000000
χ4844-4-4-2-2221-2−1−3i32−1+3i3202-11+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322-2−2i32i31-1-113-3−3−i323+i32−3+i323−i3200−i3−i3i3i300000000003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ223−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ220000000000000000
χ4944-4-4-2-2221-2−1−3i32−1+3i3202-11+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322-2−2i32i31-1-113-3−3−i323+i32−3+i323−i3200−i3−i3i3i30000000000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ220000000000000000
χ5044-4-4-2-2221-2−1−3i32−1+3i3202-11+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322-22i3−2i31-1-11-333+i32−3−i323−i32−3+i3200i3i3−i3−i300000000003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ220000000000000000
χ5144-4-4-2-2221-2−1−3i32−1+3i3202-11+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322-22i3−2i31-1-11-333+i32−3−i323−i32−3+i3200i3i3−i3−i30000000000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ223−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ220000000000000000
χ5244-4-4-2-2221-2−1+3i32−1−3i3202-11−3i321+3i321−1+3i32−1−3i32-11−3i321+3i322-2−2i32i31-1-11-333−i32−3+i323+i32−3−i3200−i3−i3i3i300000000003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ220000000000000000
χ5344-4-4-2-2221-2−1+3i32−1−3i3202-11−3i321+3i321−1+3i32−1−3i32-11−3i321+3i322-2−2i32i31-1-11-333−i32−3+i323+i32−3−i3200−i3−i3i3i30000000000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ223−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ220000000000000000
χ5444-4-4-2-2221-2−1+3i32−1−3i3202-11−3i321+3i321−1+3i32−1−3i32-11−3i321+3i322-22i3−2i31-1-113-3−3+i323−i32−3−i323+i3200i3i3−i3−i300000000003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ223−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ220000000000000000
χ5544-4-4-2-2221-2−1+3i32−1−3i3202-11−3i321+3i321−1+3i32−1−3i32-11−3i321+3i322-22i3−2i31-1-113-3−3+i323−i32−3−i323+i3200i3i3−i3−i30000000000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ220000000000000000
χ5644-4-4-2-22244-2-20-4-4224-2-2-422-44−2i32i3-222-200−2i32i32i3−2i3002i32i3−2i3−2i300000000000000000000000000000000000000
χ5744-4-4-2-22244-2-20-4-4224-2-2-422-442i3−2i3-222-2002i3−2i3−2i32i300−2i3−2i32i32i300000000000000000000000000000000000000
χ584-44-4-222-244-2-204-422-4224-2-2-4-400-2-2220000000000004-400000000000000000000000000-2200000000
χ594-44-4-222-244-2-204-422-4224-2-2-4-400-2-222000000000000-44000000000000000000000000002-200000000
χ604-4-444-44-4-21-2-20-1-2-2-22222221-1001-11-10000003i−3i3i−3i3i−3i00000000000000000000002i−2i2-20000-11−ii0000
χ614-4-444-44-4-21-2-20-1-2-2-22222221-1001-11-10000003i−3i3i−3i3i−3i0000000000000000000000−2i2i-2200001-1i−i0000
χ624-4-444-44-4-21-2-20-1-2-2-22222221-1001-11-1000000−3i3i−3i3i−3i3i00000000000000000000002i−2i-2200001-1−ii0000
χ634-4-444-44-4-21-2-20-1-2-2-22222221-1001-11-1000000−3i3i−3i3i−3i3i0000000000000000000000−2i2i2-20000-11i−i0000
χ644-4-44-22-2244-2-20-44-2-2-422-4224-400-22-22000000000000004-40000000000000000000000-220000000000
χ654-4-44-22-2244-2-20-44-2-2-422-4224-400-22-2200000000000000-4400000000000000000000002-20000000000
χ668888-4-4-4-4-422282-422-422-42222-4-4-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000
χ678888-4-4-4-4-4222-82-422-422-4222244-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000
χ6888-8-888-8-8-42-4-40-2444-4-4-4444-22002-2-2200000000000000000000000000000000000000000000000000
χ6988-8-8-4-444-42220-24-2-2-4224-2-2-22−4i34i3-111-1002i3−2i3−2i32i300i3i3−i3−i300000000000000000000000000000000000000
χ7088-8-8-4-444-42220-24-2-2-4224-2-2-224i3−4i3-111-100−2i32i32i3−2i300−i3−i3i3i300000000000000000000000000000000000000
χ718-88-88-8-882-4220-4-2-2-2-2-2-22224400-4-44400000000000000000000000000000000000000000000000000
χ728-88-88-8-88-42-4-402444444-4-4-4-2-20022-2-200000000000000000000000000000000000000000000000000
χ738-88-8-444-42-4−1−3i3−1+3i30-4-21+3i31−3i3-21+3i31−3i32−1−3i3−1+3i3440022-2-200000000000000000000000000000000000000000000000000
χ748-88-8-444-42-4−1+3i3−1−3i30-4-21−3i31+3i3-21−3i31+3i32−1+3i3−1−3i3440022-2-200000000000000000000000000000000000000000000000000
χ758-88-8-444-4-4222024-2-24-2-2-422-2-200-1-1110000000033−33−333300000000000000000000000000000000000000
χ768-88-8-444-4-4222024-2-24-2-2-422-2-200-1-11100000000−333333−3300000000000000000000000000000000000000
χ778-8-888-88-82-42204222-2-2-2-2-2-2-4400-44-4400000000000000000000000000000000000000000000000000
χ788-8-88-44-442-4−1−3i3−1+3i3042−1−3i3−1+3i3-21+3i31−3i3-21+3i31−3i3-44002-22-200000000000000000000000000000000000000000000000000
χ798-8-88-44-442-4−1+3i3−1−3i3042−1+3i3−1−3i3-21−3i31+3i3-21−3i31+3i3-44002-22-200000000000000000000000000000000000000000000000000
χ808-8-88-44-44-42220-2-4224-2-24-2-22-200-11-110000006i−6i−3i3i−3i3i00000000000000000000000000000000000000
χ818-8-88-44-44-42220-2-4224-2-24-2-22-200-11-11000000−6i6i3i−3i3i−3i00000000000000000000000000000000000000

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