Finite Group Databasebeta

← Group #13167099

Character table — Group #13167099

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size112222222444444444444444444888888888888888818182424242424242424242424242424242424243636363636727272727272108108108108
order12234466633336666666666121212123666612121212121212121212128844121212121212121212121212121212128242424242466121216161616
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
χ511-11-11-1-111111-1-1-1-1-1-11111-1-1-111-1-1-11111-1-1-1111-1-1111-111-1-1111111-1-1-1-1-1-1-111-1-11-111-1-111-1-1
χ611-11-11-1-111111-1-1-1-1-1-11111-1-1-111-1-1-11111-1-1-1111-1-1111-111-1-1111111-1-1-1-1-1-1-111-1-1-11-1-111-1-111
χ711-11-11-1-111111-1-1-1-1-1-11111-1-1-111-1-1-11111-1-1-1111-1-111-11-1-111-1-1-1-1-1-1111111-111-1-11-111-1-1-1-111
χ811-11-11-1-111111-1-1-1-1-1-11111-1-1-111-1-1-11111-1-1-1111-1-111-11-1-111-1-1-1-1-1-1111111-111-1-1-11-1-11111-1-1
χ92222222222222222222222222222222222222222222-2-2000000000000000000-2-2-2-2-20000000000
χ102222-2-222222222222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000002−22−2
χ112222-2-222222222222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000−22−22
χ12222-122-1-1-12-1-1222-1-1-1-12-1-12-122-1-12-1-1-12-1-12-1-12-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-12-1-1-1-10000000000
χ13222-122-1-1-12-1-1222-1-1-1-12-1-12-122-1-12-1-1-12-1-12-1-12-1-1-1-122-2-21111-2-21111-2-211112-1-1-1-10000000000
χ14222-122-1-1-12-1-1222-1-1-1-12-1-12-122-1-12-1-1-12-1-12-1-12-1-1-1-1-2-200−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3-211110000000000
χ15222-122-1-1-12-1-1222-1-1-1-12-1-12-122-1-12-1-1-12-1-12-1-12-1-1-1-1-2-200i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3-211110000000000
χ1622-222-2-2-222222-2-2-2-2-2-22222222-22-2-2-22-2-2-2222-2-2-22200000000000000000000000000000002−2−22
χ1722-222-2-2-222222-2-2-2-2-2-22222222-22-2-2-22-2-2-2222-2-2-2220000000000000000000000000000000−222−2
χ1822-22-22-2-222222-2-2-2-2-2-22222-2-2-222-2-2-22222-2-2-2222-2-2-2-20000000000000000002-2-2220000000000
χ1922-2-1-2211-12-1-12-2-211112-1-121-2-2-1-1-211-12-1-1-2112-1-111222-2-1-11122-1-1-1-1-2-21111-2-1-1110000000000
χ2022-2-1-2211-12-1-12-2-211112-1-121-2-2-1-1-211-12-1-1-2112-1-11122-2211-1-1-2-2111122-1-1-1-1-2-1-1110000000000
χ2122-2-1-2211-12-1-12-2-211112-1-121-2-2-1-1-211-12-1-1-2112-1-111-2-200−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3211-1-10000000000
χ2222-2-1-2211-12-1-12-2-211112-1-121-2-2-1-1-211-12-1-1-2112-1-111-2-200i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3211-1-10000000000
χ23444444444111-2111111111-24-2-24-2-2-2-2-2111111-2-2-2-2-200222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000
χ24444444444111-2111111111-24-2-24-2-2-2-2-2111111-2-2-2-2-200-2-2-2-2-2-2111111111111000000000000000
χ25444444444-2-2-21-2-2-2-2-2-2-2-2-21411411111-2-2-2-2-2-211111000000000000000000000000022-1-1-1-10000
χ26444444444-2-2-21-2-2-2-2-2-2-2-2-21411411111-2-2-2-2-2-2111110000000000000000000000000-2-211110000
χ274444-4-4444111-2111111111-2-422-4-2-2-2-2-2-1-1-1-1-1-12222200000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000
χ284444-4-4444111-2111111111-2-422-4-2-2-2-2-2-1-1-1-1-1-12222200000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000000
χ294444-4-4444-2-2-21-2-2-2-2-2-2-2-2-21-4-1-1-411111222222-1-1-1-1-1000000000000000000000000000−i3i3−i3i30000
χ304444-4-4444-2-2-21-2-2-2-2-2-2-2-2-21-4-1-1-411111222222-1-1-1-1-1000000000000000000000000000i3−i3i3−i30000
χ31444-244-2-2-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-2-2-2-2-21-21111−1−3i32−1+3i321−1−3i32−1+3i32-211110022−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000000
χ32444-244-2-2-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-2-2-2-2-21-21111−1−3i32−1+3i321−1−3i32−1+3i32-2111100-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000000
χ33444-244-2-2-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32-2-2-2-2-21-21111−1+3i32−1−3i321−1+3i32−1−3i32-211110022−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000000
χ34444-244-2-2-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32-2-2-2-2-21-21111−1+3i32−1−3i321−1+3i32−1−3i32-2111100-2-21−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000000
χ35444-2-4-4-2-2-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-222221-2111-11+3i321−3i32-11+3i321−3i322-1-1-1-100000000−i3i3−3+i323−i323+i32−3−i32−i3i3−3+i323−i323+i32−3−i32000000000000000
χ36444-2-4-4-2-2-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-222221-2111-11+3i321−3i32-11+3i321−3i322-1-1-1-100000000i3−i33−i32−3+i32−3−i323+i32i3−i33−i32−3+i32−3−i323+i32000000000000000
χ37444-2-4-4-2-2-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32-222221-2111-11−3i321+3i32-11−3i321+3i322-1-1-1-100000000−i3i33+i32−3−i32−3+i323−i32−i3i33+i32−3−i32−3+i323−i32000000000000000
χ38444-2-4-4-2-2-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32-222221-2111-11−3i321+3i32-11−3i321+3i322-1-1-1-100000000i3−i3−3−i323+i323−i32−3+i32i3−i3−3−i323+i323−i32−3+i32000000000000000
χ39444-2-4-4-2-2-24-2-2444-2-2-2-24-2-242-4-42-24-2-2-2-422-422-4222200000000000000000000000000000000000
χ4044-444-4-4-44111-2-1-1-1-1-1-1111-24-2-2-4-2222-2-1-1-1111222-2-200000000−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3000000000000000
χ4144-444-4-4-44111-2-1-1-1-1-1-1111-24-2-2-4-2222-2-1-1-1111222-2-200000000i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3000000000000000
χ4244-444-4-4-44-2-2-21222222-2-2-21411-41-1-1-11222-2-2-2-1-1-111000000000000000000000000000−i3i3i3−i30000
χ4344-444-4-4-44-2-2-21222222-2-2-21411-41-1-1-11222-2-2-2-1-1-111000000000000000000000000000i3−i3−i3i30000
χ4444-44-44-4-44111-2-1-1-1-1-1-1111-2-4224-2222-2111-1-1-1-2-2-222002-222-2-2-1-1-1-1-1-1111111000000000000000
χ4544-44-44-4-44111-2-1-1-1-1-1-1111-2-4224-2222-2111-1-1-1-2-2-22200-22-2-222111111-1-1-1-1-1-1000000000000000
χ4644-44-44-4-44-2-2-21222222-2-2-21-4-1-141-1-1-11-2-2-2222111-1-100000000000000000000000002-2-1-1110000
χ4744-44-44-4-44-2-2-21222222-2-2-21-4-1-141-1-1-11-2-2-2222111-1-10000000000000000000000000-2211-1-10000
χ4844-4-24-422-21−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i321−1−3i32−1+3i32-2-2-2-2212-1-11-11+3i321−3i321−1−3i32−1+3i322-1-11100000000−i3i3−3+i323−i323+i32−3−i32i3−i33−i32−3+i32−3−i323+i32000000000000000
χ4944-4-24-422-21−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i321−1−3i32−1+3i32-2-2-2-2212-1-11-11+3i321−3i321−1−3i32−1+3i322-1-11100000000i3−i33−i32−3+i32−3−i323+i32−i3i3−3+i323−i323+i32−3−i32000000000000000
χ5044-4-24-422-21−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i321−1+3i32−1−3i32-2-2-2-2212-1-11-11−3i321+3i321−1+3i32−1−3i322-1-11100000000−i3i33+i32−3−i32−3+i323−i32i3−i3−3−i323+i323−i32−3+i32000000000000000
χ5144-4-24-422-21−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i321−1+3i32−1−3i32-2-2-2-2212-1-11-11−3i321+3i321−1+3i32−1−3i322-1-11100000000i3−i3−3−i323+i323−i32−3+i32−i3i33+i32−3−i32−3+i323−i32000000000000000
χ5244-4-24-422-24-2-24-4-422224-2-24-2442-2-422-2-4224-2-2-422-2-200000000000000000000000000000000000
χ5344-4-2-4422-21−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i321−1−3i32−1+3i32-2222-212-1-111−1−3i32−1+3i32-11+3i321−3i32-211-1-1002-2−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000000
χ5444-4-2-4422-21−1−3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i321−1−3i32−1+3i32-2222-212-1-111−1−3i32−1+3i32-11+3i321−3i32-211-1-100-221+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000000
χ5544-4-2-4422-21−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i321−1+3i32−1−3i32-2222-212-1-111−1+3i32−1−3i32-11−3i321+3i32-211-1-1002-2−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000000
χ5644-4-2-4422-21−1+3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i321−1+3i32−1−3i32-2222-212-1-111−1+3i32−1−3i32-11−3i321+3i32-211-1-100-221−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000000
χ574-4040000-44444000000-4-4-4-400004000-40000000000022−22000000000000000000022−22000000000000
χ584-4040000-44444000000-4-4-4-400004000-400000000000−22220000000000000000000−2222000000000000
χ594-40-200−2i32i324-2-2400−2i32i3−2i32i3-422-40000-20−2i32i320000000000022−220000000000000000000−22i6−i60000000000
χ604-40-200−2i32i324-2-2400−2i32i3−2i32i3-422-40000-20−2i32i3200000000000−222200000000000000000002−2−i6i60000000000
χ614-40-2002i3−2i324-2-24002i3−2i32i3−2i3-422-40000-202i3−2i320000000000022−220000000000000000000−22−i6i60000000000
χ624-40-2002i3−2i324-2-24002i3−2i32i3−2i3-422-40000-202i3−2i3200000000000−222200000000000000000002−2i6−i60000000000
χ63888-488-4-4-4-4222-4-42222-4222-422-4-12-1-1-1-422-4222-1-1-1-100000000000000000000000000000000000
χ64888-4-8-8-4-4-4-4222-4-42222-42224-2-24-12-1-1-14-2-24-2-2-2111100000000000000000000000000000000000
χ6588-8-48-844-4-422244-2-2-2-2-4222-4224-1-211-14-2-2-422-211-1-100000000000000000000000000000000000
χ6688-8-4-8844-4-422244-2-2-2-2-42224-2-2-4-1-211-1-4224-2-22-1-11100000000000000000000000000000000000
χ678-8080000-8222-46-66-6-66-2-2-240000-400040000000000000000000000000000000000000000000000
χ688-8080000-8222-4-66-666-6-2-2-240000-400040000000000000000000000000000000000000000000000
χ698-8080000-8-4-4-42000000444-206i−6i02000-20000000006i−6i00000000000000000000000000000000000
χ708-8080000-8-4-4-42000000444-20−6i6i02000-2000000000−6i6i00000000000000000000000000000000000
χ718-80-400−4i34i342−1−3i3−1+3i3-46-6−3−i33+i33−i3−3+i3-21+3i31−3i340000202i3−2i3-20000000000000000000000000000000000000000000000
χ728-80-400−4i34i342−1+3i3−1−3i3-4-663−i3−3+i3−3−i33+i3-21−3i31+3i340000202i3−2i3-20000000000000000000000000000000000000000000000
χ738-80-400−4i34i34-4222002i3−2i32i3−2i34-2-2-206i−6i0-10−i3i31000000033−33−3i3i00000000000000000000000000000000000
χ748-80-400−4i34i34-4222002i3−2i32i3−2i34-2-2-20−6i6i0-10−i3i310000000−33333i−3i00000000000000000000000000000000000
χ758-80-4004i3−4i342−1−3i3−1+3i3-4-663+i3−3−i3−3+i33−i3-21+3i31−3i34000020−2i32i3-20000000000000000000000000000000000000000000000
χ768-80-4004i3−4i342−1+3i3−1−3i3-46-6−3+i33−i33+i3−3−i3-21−3i31+3i34000020−2i32i3-20000000000000000000000000000000000000000000000
χ778-80-4004i3−4i34-422200−2i32i3−2i32i34-2-2-206i−6i0-10i3−i310000000−3333−3i3i00000000000000000000000000000000000
χ788-80-4004i3−4i34-422200−2i32i3−2i32i34-2-2-20−6i6i0-10i3−i31000000033−333i−3i00000000000000000000000000000000000

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