Finite Group Databasebeta

← Group #13167041

Character table — Group #13167041

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122224444444444444444444888888888888888818182424242424242424242424242424242424243636363636727272727272108108108108
order12223666333346666666666661212366612121212121212121212121244441212121212121212121212121212121241212121244121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111
χ5111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1111111-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1
χ6111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1111111-1-1-1-1-1-1-1-1-111-1111-1-1-1-111
χ7111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1-1-1-1-1111111-1-1-1111-1-1-111-1-111
χ8111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1-1-1-1-1111111-1-1-111-1111-1-111-1-1
χ92222222222222222222222222222222222222222222-2-2000000000000000000-2-2-2-2-20000000000
χ10222222222222-2222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000222-2-20000000000
χ112222-1-1-1-122-1-1222-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-12-1-1-1-10000000000
χ122222-1-1-1-122-1-1222-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-122-2-21111-2-21111-2-211112-1-1-1-10000000000
χ132222-1-1-1-122-1-1222-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-200−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3-211110000000000
χ142222-1-1-1-122-1-1222-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-200i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3-211110000000000
χ152222-1-1-1-122-1-1-222-1-12-1-12-1-12211-1-1-1-1-2-21111-2-21111222-2-1-11122-1-1-1-1-2-21111-211-1-10000000000
χ162222-1-1-1-122-1-1-222-1-12-1-12-1-12211-1-1-1-1-2-21111-2-2111122-2211-1-1-2-2111122-1-1-1-1-211-1-10000000000
χ172222-1-1-1-122-1-1-222-1-12-1-12-1-12211-1-1-1-1-2-21111-2-21111-2-200−i3i3i3−i300−i3−i3i3i300i3i3−i3−i32-1-1110000000000
χ182222-1-1-1-122-1-1-222-1-12-1-12-1-12211-1-1-1-1-2-21111-2-21111-2-200i3−i3−i3i300i3i3−i3−i300−i3−i3i3i32-1-1110000000000
χ192-22-22-2-22222202-2-2-2-2-2-2222-2-20022-2-20000000000002-20000000000000000000002-2000000002i−2i
χ202-22-22-2-22222202-2-2-2-2-2-2222-2-20022-2-20000000000002-20000000000000000000002-200000000−2i2i
χ212-22-22-2-22222202-2-2-2-2-2-2222-2-20022-2-2000000000000-22000000000000000000000-220000002i−2i00
χ222-22-22-2-22222202-2-2-2-2-2-2222-2-20022-2-2000000000000-22000000000000000000000-22000000−2i2i00
χ23444444441-2114-2111111111-2-244-2-2-2-2111111-2-2-2-2-2-200222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000
χ24444444441-2114-2111111111-2-244-2-2-2-2111111-2-2-2-2-2-200-2-2-2-2-2-2111111111111000000000000000
χ25444444441-211-4-2111111111-2-2-4-4-2-2-2-2-1-1-1-1-1-1222222002-222-2-2-1-1-1-1-1-1111111000000000000000
χ26444444441-211-4-2111111111-2-2-4-4-2-2-2-2-1-1-1-1-1-122222200-22-2-222111111-1-1-1-1-1-1000000000000000
χ2744444444-21-2-241-2-2-2-2-2-2-2-2-211441111-2-2-2-2-2-2111111000000000000000000000000022-1-1-1-10000
χ2844444444-21-2-241-2-2-2-2-2-2-2-2-211441111-2-2-2-2-2-21111110000000000000000000000000-2-211110000
χ2944444444-21-2-2-41-2-2-2-2-2-2-2-2-211-4-41111222222-1-1-1-1-1-100000000000000000000000002-211-1-10000
χ3044444444-21-2-2-41-2-2-2-2-2-2-2-2-211-4-41111222222-1-1-1-1-1-10000000000000000000000000-22-1-1110000
χ314444-2-2-2-21-2−1−3i32−1+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+3i32-2-211110022−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000000
χ324444-2-2-2-21-2−1−3i32−1+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+3i32-2-2111100-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000000
χ334444-2-2-2-21-2−1−3i32−1+3i32-4-21−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2221111-1-11+3i321+3i321−3i321−3i3222-1-1-1-1002-2−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000000
χ344444-2-2-2-21-2−1−3i32−1+3i32-4-21−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2221111-1-11+3i321+3i321−3i321−3i3222-1-1-1-100-221+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000000
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+3i32−1−3i32−1−3i32-2-211110022−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000000
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+3i32−1−3i32−1−3i32-2-2111100-2-21−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000000
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+3i3222-1-1-1-1002-2−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000000
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+3i3222-1-1-1-100-221−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000000
χ3944-4-444-4-41-21102-1-1-1111-1-1-12-200-222-23-33-33-3000000000000003−33−33−33−33−33−3000000000000000
χ4044-4-444-4-41-21102-1-1-1111-1-1-12-200-222-23-33-33-300000000000000−33−33−33−33−33−33000000000000000
χ4144-4-444-4-41-21102-1-1-1111-1-1-12-200-222-2-33-33-33000000000000003−33−33−3−33−33−33000000000000000
χ4244-4-444-4-41-21102-1-1-1111-1-1-12-200-222-2-33-33-3300000000000000−33−33−333−33−33−3000000000000000
χ4344-4-444-4-444440-4-4-4-4444-4-4-4-44004-4-4400000000000000000000000000000000000000000000000
χ4444-4-4-2-2221-2−1−3i32−1+3i3202-11+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322-2−2i32i31-1-113-3−3−i323+i32−3+i323−i3200−i3−i3i3i3000000003−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ113−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000000000000
χ4544-4-4-2-2221-2−1−3i32−1+3i3202-11+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322-2−2i32i31-1-113-3−3−i323+i32−3+i323−i3200−i3−i3i3i300000000−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000000000000
χ4644-4-4-2-2221-2−1−3i32−1+3i3202-11+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322-22i3−2i31-1-11-333+i32−3−i323−i32−3+i3200i3i3−i3−i3000000003−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000000000000
χ4744-4-4-2-2221-2−1−3i32−1+3i3202-11+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322-22i3−2i31-1-11-333+i32−3−i323−i32−3+i3200i3i3−i3−i300000000−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ113−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000000000000
χ4844-4-4-2-2221-2−1+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−i3i3i3000000003−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000000000000
χ4944-4-4-2-2221-2−1+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−i3i3i300000000−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ113−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000000000000
χ5044-4-4-2-2221-2−1+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−i3000000003−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ113−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000000000000
χ5144-4-4-2-2221-2−1+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−i300000000−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000000000000
χ5244-4-4-2-22244-2-20-4-4224-2-2-422-44−2i32i3-222-200−2i32i32i3−2i3002i32i3−2i3−2i300000000000000000000000000000000000
χ5344-4-4-2-22244-2-20-4-4224-2-2-422-442i3−2i3-222-2002i3−2i3−2i32i300−2i3−2i32i32i300000000000000000000000000000000000
χ544-44-4-222-244-2-204-422-4224-2-2-4-400-2-2220000000000004-4000000000000000000000-220000000000
χ554-44-4-222-244-2-204-422-4224-2-2-4-400-2-222000000000000-440000000000000000000002-20000000000
χ564-4-444-44-444440-4444-4-4-4-4-4-44-4004-44-400000000000000000000000000000000000000000000000
χ574-4-444-44-4-21-2-20-1-2-2-22222221-1001-11-10000003i−3i3i−3i3i−3i000000000000000000000000000−i3i33−30000
χ584-4-444-44-4-21-2-20-1-2-2-22222221-1001-11-10000003i−3i3i−3i3i−3i000000000000000000000000000i3−i3−330000
χ594-4-444-44-4-21-2-20-1-2-2-22222221-1001-11-1000000−3i3i−3i3i−3i3i000000000000000000000000000−i3i3−330000
χ604-4-444-44-4-21-2-20-1-2-2-22222221-1001-11-1000000−3i3i−3i3i−3i3i000000000000000000000000000i3−i33−30000
χ614-4-44-22-2244-2-20-44-2-2-422-4224-400-22-22000000000000000000000000000000000−2i32i3000000000000
χ624-4-44-22-2244-2-20-44-2-2-422-4224-400-22-220000000000000000000000000000000002i3−2i3000000000000
χ638888-4-4-4-4-422282-422-422-42222-4-4-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000
χ648888-4-4-4-4-4222-82-422-422-4222244-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000
χ6588-8-888-8-8-42-4-40-2444-4-4-4444-22002-2-2200000000000000000000000000000000000000000000000
χ6688-8-8-4-444-42220-24-2-2-4224-2-2-22−4i34i3-111-1002i3−2i3−2i32i300i3i3−i3−i300000000000000000000000000000000000
χ6788-8-8-4-444-42220-24-2-2-4224-2-2-224i3−4i3-111-100−2i32i32i3−2i300−i3−i3i3i300000000000000000000000000000000000
χ688-88-88-8-882-4220-4-2-2-2-2-2-22224400-4-44400000000000000000000000000000000000000000000000
χ698-88-88-8-88-42-4-402444444-4-4-4-2-20022-2-200000000000000000000000000000000000000000000000
χ708-88-8-444-42-4−1−3i3−1+3i30-4-21+3i31−3i3-21+3i31−3i32−1−3i3−1+3i3440022-2-200000000000000000000000000000000000000000000000
χ718-88-8-444-42-4−1+3i3−1−3i30-4-21−3i31+3i3-21−3i31+3i32−1+3i3−1−3i3440022-2-200000000000000000000000000000000000000000000000
χ728-88-8-444-4-4222024-2-24-2-2-422-2-200-1-1110000000033−33−333300000000000000000000000000000000000
χ738-88-8-444-4-4222024-2-24-2-2-422-2-200-1-11100000000−333333−3300000000000000000000000000000000000
χ748-8-888-88-82-42204222-2-2-2-2-2-2-4400-44-4400000000000000000000000000000000000000000000000
χ758-8-88-44-442-4−1−3i3−1+3i3042−1−3i3−1+3i3-21+3i31−3i3-21+3i31−3i3-44002-22-200000000000000000000000000000000000000000000000
χ768-8-88-44-442-4−1+3i3−1−3i3042−1+3i3−1−3i3-21−3i31+3i3-21−3i31+3i3-44002-22-200000000000000000000000000000000000000000000000
χ778-8-88-44-44-42220-2-4224-2-24-2-22-200-11-110000006i−6i−3i3i−3i3i00000000000000000000000000000000000
χ788-8-88-44-44-42220-2-4224-2-24-2-22-200-11-11000000−6i6i3i−3i3i−3i00000000000000000000000000000000000

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