Finite Group Databasebeta

← Group #13167101

Character table — Group #13167101

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size112222222444444444444444444888888888888888818182424242424242424242424242424242424243636363636727272727272108108108108
order12234461212333366666661212121212121236666661212121212121212128824666666661212121212121212824242424441212121216161616
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
χ511-11-111-1-11111-1-1-11111-1-1-1-1-1-111-1-1-1-1-111111-111-1-1111-111111111-1-1-1-1-1-1-1-1-111-1-11-111-1-111-1-1
χ611-11-111-1-11111-1-1-11111-1-1-1-1-1-111-1-1-1-1-111111-111-1-1111-111111111-1-1-1-1-1-1-1-1-111-1-1-11-1-111-1-111
χ711-11-111-1-11111-1-1-11111-1-1-1-1-1-111-1-1-1-1-111111-111-1-111-11-1-1-1-1-1-1-1-111111111-111-1-11-111-1-1-1-111
χ811-11-111-1-11111-1-1-11111-1-1-1-1-1-111-1-1-1-1-111111-111-1-111-11-1-1-1-1-1-1-1-111111111-111-1-1-11-1-11111-1-1
χ92222222222222222222222222222222222222222222-2-2000000000000000000-2-2-2-2-20000000000
χ102222-2-22-2-222222222222-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-200000000000000000000000000000002−22−2
χ112222-2-22-2-222222222222-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-20000000000000000000000000000000−22−22
χ12222-122-1-1-122-1-1-1222-1-1222-1-1-1-1-1-12-1-1-1-1-12-1-122-1-1-1-12222-1-122-1-1-1-1-1-122-1-1-1-12-1-1-1-10000000000
χ13222-122-1-1-122-1-1-1222-1-1222-1-1-1-1-1-12-1-1-1-1-12-1-122-1-1-1-122-2-211-2-2111111-2-211112-1-1-1-10000000000
χ14222-122-1-1-122-1-1-1222-1-1222-1-1-1-1-1-12-1-1-1-1-12-1-122-1-1-1-1-2-200−i3i300−i3−i3i3i3−i3i300−i3−i3i3i3-211110000000000
χ15222-122-1-1-122-1-1-1222-1-1222-1-1-1-1-1-12-1-1-1-1-12-1-122-1-1-1-1-2-200i3−i300i3i3−i3−i3i3−i300i3i3−i3−i3-211110000000000
χ1622-222-22222222-2-2-22222222222-22-2-2-2-2-22-2-2-2-22-2-22200000000000000000000000000000002−2−22
χ1722-222-22222222-2-2-22222222222-22-2-2-2-2-22-2-2-2-22-2-2220000000000000000000000000000000−222−2
χ1822-22-222-2-22222-2-2-22222-2-2-2-2-2-222-2-2-2-2-222222-222-2-2-2-20000000000000000002-2-2220000000000
χ1922-2-1-22-11122-1-11-2-22-1-12-2-21111-1-1-21111-12-1-12-2-1-111222-2-1-122-1-1-1-111-2-21111-2-1-1110000000000
χ2022-2-1-22-11122-1-11-2-22-1-12-2-21111-1-1-21111-12-1-12-2-1-11122-2211-2-21111-1-122-1-1-1-1-2-1-1110000000000
χ2122-2-1-22-11122-1-11-2-22-1-12-2-21111-1-1-21111-12-1-12-2-1-111-2-200−i3i300−i3−i3i3i3i3−i300i3i3−i3−i3211-1-10000000000
χ2222-2-1-22-11122-1-11-2-22-1-12-2-21111-1-1-21111-12-1-12-2-1-111-2-200i3−i300i3i3−i3−i3−i3i300−i3−i3i3i3211-1-10000000000
χ234444444441-2-2-2411-2-2-21-2-2-2-2-2-241-2-2-2111-2-2-2111111000000000000000000000000022-1-1-1-10000
χ244444444441-2-2-2411-2-2-21-2-2-2-2-2-241-2-2-2111-2-2-21111110000000000000000000000000-2-211110000
χ25444444444-21114-2-2111-21111114-2111-2-2-2111-2-2-2-2-2-2002222-1-1-1-1-1-122-1-1-1-1-1-1000000000000000
χ26444444444-21114-2-2111-21111114-2111-2-2-2111-2-2-2-2-2-200-2-2-2-2111111-2-2111111000000000000000
χ274444-4-44-4-41-2-2-2411-2-2-21222222-41-2-2-2111222-1-1-1-1-1-1000000000000000000000000000−i3i3−i3i30000
χ284444-4-44-4-41-2-2-2411-2-2-21222222-41-2-2-2111222-1-1-1-1-1-1000000000000000000000000000i3−i3i3−i30000
χ294444-4-44-4-4-21114-2-2111-2-1-1-1-1-1-1-4-2111-2-2-2-1-1-1222222000000−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000000000000
χ304444-4-44-4-4-21114-2-2111-2-1-1-1-1-1-1-4-2111-2-2-2-1-1-1222222000000i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000000
χ31444-244-2-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i32-211−1−3i32−1+3i321111−1−3i32−1+3i32-2-211110022−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32000000000000000
χ32444-244-2-2-2-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i32-211−1−3i32−1+3i321111−1−3i32−1+3i32-2-2111100-2-21+i31−i311−1−i32−1−i32−1+i32−1+i321+i31−i311−1−i32−1−i32−1+i32−1+i32000000000000000
χ33444-244-2-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i32-211−1+3i32−1−3i321111−1+3i32−1−3i32-2-211110022−1+i3−1−i3-1-11−i321−i321+i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32000000000000000
χ34444-244-2-2-2-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i32-211−1+3i32−1−3i321111−1+3i32−1−3i32-2-2111100-2-21−i31+i311−1+i32−1+i32−1−i32−1−i321−i31+i311−1+i32−1+i32−1−i32−1−i32000000000000000
χ35444-2-4-4-22244-2-2-2444-2-24-4-422222-24-2-2-2-2-2-422-4-4222200000000000000000000000000000000000
χ36444-2-4-4-222-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i32211−1−3i32−1+3i32111-11+3i321−3i3222-1-1-1-1000000−i3i3−3+i323−i323+i32−3−i3200−i3i3−3+i323−i323+i32−3−i32000000000000000
χ37444-2-4-4-222-21−1−3i32−1+3i32-2-2-21−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i32211−1−3i32−1+3i32111-11+3i321−3i3222-1-1-1-1000000i3−i33−i32−3+i32−3−i323+i3200i3−i33−i32−3+i32−3−i323+i32000000000000000
χ38444-2-4-4-222-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i32211−1+3i32−1−3i32111-11−3i321+3i3222-1-1-1-1000000−i3i33+i32−3−i32−3+i323−i3200−i3i33+i32−3−i32−3+i323−i32000000000000000
χ39444-2-4-4-222-21−1+3i32−1−3i32-2-2-21−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i32211−1+3i32−1−3i32111-11−3i321+3i3222-1-1-1-1000000i3−i3−3−i323+i323−i32−3+i3200i3−i3−3−i323+i323−i32−3+i32000000000000000
χ4044-444-44441-2-2-2-4-1-1-2-2-21-2-2-2-2-2-2-41222-1-11222-11-1-111000000000000000000000000000−i3i3i3−i30000
χ4144-444-44441-2-2-2-4-1-1-2-2-21-2-2-2-2-2-2-41222-1-11222-11-1-111000000000000000000000000000i3−i3−i3i30000
χ4244-444-4444-2111-422111-2111111-4-2-1-1-122-2-1-1-12-222-2-2000000−i3i3−i3i3−i3i300i3−i3i3−i3i3−i3000000000000000
χ4344-444-4444-2111-422111-2111111-4-2-1-1-122-2-1-1-12-222-2-2000000i3−i3i3−i3i3−i300−i3i3−i3i3−i3i3000000000000000
χ4444-44-444-4-41-2-2-2-4-1-1-2-2-2122222241222-1-11-2-2-21-111-1-100000000000000000000000002-2-1-1110000
χ4544-44-444-4-41-2-2-2-4-1-1-2-2-2122222241222-1-11-2-2-21-111-1-10000000000000000000000000-2211-1-10000
χ4644-44-444-4-4-2111-422111-2-1-1-1-1-1-14-2-1-1-122-2111-22-2-222002-222-1-1-1-1-1-1-2-2111111000000000000000
χ4744-44-444-4-4-2111-422111-2-1-1-1-1-1-14-2-1-1-122-2111-22-2-22200-22-2-211111122-1-1-1-1-1-1000000000000000
χ4844-4-24-4-2-2-244-2-22-4-44-2-2444-2-2-2-22-2-42222-2-422-4422-2-200000000000000000000000000000000000
χ4944-4-24-4-2-2-2-21−1−3i32−1+3i322221−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i3221-11+3i321−3i32-1-11-11+3i321−3i322-2-1-111000000−i3i3−3+i323−i323+i32−3−i3200i3−i33−i32−3+i32−3−i323+i32000000000000000
χ5044-4-24-4-2-2-2-21−1−3i32−1+3i322221−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i3221-11+3i321−3i32-1-11-11+3i321−3i322-2-1-111000000i3−i33−i32−3+i32−3−i323+i3200−i3i3−3+i323−i323+i32−3−i32000000000000000
χ5144-4-24-4-2-2-2-21−1+3i32−1−3i322221−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i3221-11−3i321+3i32-1-11-11−3i321+3i322-2-1-111000000−i3i33+i32−3−i32−3+i323−i3200i3−i3−3−i323+i323−i32−3+i32000000000000000
χ5244-4-24-4-2-2-2-21−1+3i32−1−3i322221−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i3221-11−3i321+3i32-1-11-11−3i321+3i322-2-1-111000000i3−i3−3−i323+i323−i32−3+i3200−i3i33+i32−3−i32−3+i323−i32000000000000000
χ5344-4-2-44-222-21−1−3i32−1+3i322221−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i32-21-11+3i321−3i32-1-111−1−3i32−1+3i32-2211-1-1002-2−1−i3−1+i3-1-11+i321+i321−i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i32000000000000000
χ5444-4-2-44-222-21−1−3i32−1+3i322221−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i32-21-11+3i321−3i32-1-111−1−3i32−1+3i32-2211-1-100-221+i31−i311−1−i32−1−i32−1+i32−1+i32−1−i3−1+i3-1-11+i321+i321−i321−i32000000000000000
χ5544-4-2-44-222-21−1+3i32−1−3i322221−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i32-21-11−3i321+3i32-1-111−1+3i32−1−3i32-2211-1-1002-2−1+i3−1−i3-1-11−i321−i321+i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i32000000000000000
χ5644-4-2-44-222-21−1+3i32−1−3i322221−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i32-21-11−3i321+3i32-1-111−1+3i32−1−3i32-2211-1-100-221−i31+i311−1+i32−1+i32−1−i32−1−i32−1+i3−1−i3-1-11−i321−i321+i321+i32000000000000000
χ574-40400-4004444000-4-4-4-40000000400000-400000000022−22000000000000000000022−22000000000000
χ584-40400-4004444000-4-4-4-40000000400000-4000000000−22220000000000000000000−2222000000000000
χ594-40-200223−2344-2-2000-422-40023−2323−230-2000002000000023−2322−220000000000000000000−226−60000000000
χ604-40-200223−2344-2-2000-422-40023−2323−230-2000002000000023−23−222200000000000000000002−2−660000000000
χ614-40-2002−232344-2-2000-422-400−2323−23230-20000020000000−232322−220000000000000000000−22−660000000000
χ624-40-2002−232344-2-2000-422-400−2323−23230-20000020000000−2323−222200000000000000000002−26−60000000000
χ63888-488-4-4-42-422-422-4222-4-42222-4-1-422-1-1-1-42222-1-1-1-100000000000000000000000000000000000
χ64888-4-8-8-4442-422-422-422244-2-2-2-24-1-422-1-1-14-2-2-2-2111100000000000000000000000000000000000
χ6588-8-48-8-4-4-42-4224-2-2-4222-4-422224-14-2-211-14-2-2-2211-1-100000000000000000000000000000000000
χ6688-8-4-88-4442-4224-2-2-422244-2-2-2-2-4-14-2-211-1-4222-2-1-11100000000000000000000000000000000000
χ678-80800-8002-4-4-406-6444-2000000020006-6-200000000000000000000000000000000000000000000
χ688-80800-8002-4-4-40-66444-200000002000-66-200000000000000000000000000000000000000000000
χ698-80800-800-4222000-2-2-246i−6i6i−6i−6i6i0-400000400000000000000000000000000000000000000000000
χ708-80800-800-4222000-2-2-24−6i6i−6i6i6i−6i0-400000400000000000000000000000000000000000000000000
χ718-80-400443−432-42206-64-2-2-200−2323−23230-1000-3310000033−333−300000000000000000000000000000000000
χ728-80-400443−432-4220-664-2-2-200−2323−23230-10003-3100000−33333−300000000000000000000000000000000000
χ738-80-400443−43-42−1−3i3−1+3i3000-21+3i31−3i346i−6i2ζ14+4ζ22−2ζ14−4ζ22−4ζ14−2ζ224ζ14+2ζ220200000-20000000−232300000000000000000000000000000000000
χ748-80-400443−43-42−1+3i3−1−3i3000-21−3i31+3i34−6i6i−4ζ14−2ζ224ζ14+2ζ222ζ14+4ζ22−2ζ14−4ζ220200000-20000000−232300000000000000000000000000000000000
χ758-80-4004−43432-42206-64-2-2-20023−2323−230-1000-33100000−3333−3300000000000000000000000000000000000
χ768-80-4004−43432-4220-664-2-2-20023−2323−230-10003-310000033−33−3300000000000000000000000000000000000
χ778-80-4004−4343-42−1−3i3−1+3i3000-21+3i31−3i34−6i6i−2ζ14−4ζ222ζ14+4ζ224ζ14+2ζ22−4ζ14−2ζ220200000-2000000023−2300000000000000000000000000000000000
χ788-80-4004−4343-42−1+3i3−1−3i3000-21−3i31+3i346i−6i4ζ14+2ζ22−4ζ14−2ζ22−2ζ14−4ζ222ζ14+4ζ220200000-2000000023−2300000000000000000000000000000000000

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