Finite Group Databasebeta

← Group #10691621

Character table — Group #10691621

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212121212121616161616161616161624242424242424244848
order1222222222344666444666666121212124444888812122424242424242424444444444412121212121212124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ611111111111111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-11111-1-1
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-111
χ9111111-1-1-1-11111111-1-111-1-1-1-11111ii−i−i11-1-1-1-11111-1-1-1-111-1-1ii−i−ii−iii−i−iii−i−i1-1i−iii−i−i1-1
χ10111111-1-1-1-11111111-1-111-1-1-1-11111ii−i−i11-1-1-1-11111-1-1-1-1-1-111−i−iiii−iii−i−iii−i−i-11−ii−i−iii-11
χ11111111-1-1-1-11111111-1-111-1-1-1-11111ii−i−i-1-111-1-1-1-1-1-1111111-1-1ii−i−i−iiii−i−i−i−iii1-1i−i−i−iii-11
χ12111111-1-1-1-11111111-1-111-1-1-1-11111ii−i−i-1-111-1-1-1-1-1-11111-1-111−i−iii−iiii−i−i−i−iii-11−iiii−i−i1-1
χ13111111-1-1-1-11111111-1-111-1-1-1-11111−i−iii11-1-1-1-11111-1-1-1-111-1-1−i−iii−ii−i−iii−i−iii1-1−ii−i−iii1-1
χ14111111-1-1-1-11111111-1-111-1-1-1-11111−i−iii11-1-1-1-11111-1-1-1-1-1-111ii−i−i−ii−i−iii−i−iii-11i−iii−i−i-11
χ15111111-1-1-1-11111111-1-111-1-1-1-11111−i−iii-1-111-1-1-1-1-1-1111111-1-1−i−iiii−i−i−iiiii−i−i1-1−iiii−i−i-11
χ16111111-1-1-1-11111111-1-111-1-1-1-11111−i−iii-1-111-1-1-1-1-1-11111-1-111ii−i−ii−i−i−iiiii−i−i-11i−i−i−iii1-1
χ1722222222222-2-2222-2-2-2222222-2-2-2-200000000-2-20000000000002222000000000000-2-2000000
χ1822222222222-2-2222-2-2-2222222-2-2-2-200000000-2-2000000000000-2-2-2-200000000000022000000
χ192222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-10000000000
χ202222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-11111111100000000-2-2-1-1-1-111110000000000
χ212222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100000000-2-2111111110000000000
χ222222222222-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111111100000000221111-1-1-1-10000000000
χ23222222-2-2-2-22-2-2222-22222-2-2-2-2-2-2-2-200000000220000000000002i2i−2i−2i000000000000−2i2i000000
χ24222222-2-2-2-22-2-2222-22222-2-2-2-2-2-2-2-20000000022000000000000−2i−2i2i2i0000000000002i−2i000000
χ25222222-2-2-2-2-122-1-1-12-2-2-1-11111-1-1-1-12i2i−2i−2i22-2-211-1-1-1-11111000000002i−2i−i−iii−i−iii0000000000
χ26222222-2-2-2-2-122-1-1-12-2-2-1-11111-1-1-1-12i2i−2i−2i-2-222111111-1-1-1-100000000−2i2i−i−iiiii−i−i0000000000
χ27222222-2-2-2-2-122-1-1-12-2-2-1-11111-1-1-1-1−2i−2i2i2i22-2-211-1-1-1-1111100000000−2i2iii−i−iii−i−i0000000000
χ28222222-2-2-2-2-122-1-1-12-2-2-1-11111-1-1-1-1−2i−2i2i2i-2-222111111-1-1-1-1000000002i−2iii−i−i−i−iii0000000000
χ292222-2-222-2-2222222-2-22-2-22-22-2-2-222000000002-20000000022-2-200000000000000-2200000000
χ302222-2-222-2-2222222-2-22-2-22-22-2-2-222000000002-200000000-2-222000000000000002-200000000
χ312222-2-222-2-22-2-222222-2-2-22-22-222-2-22i−2i2i−2i0000-220000000000000000002i−2i2i−2i00000000000000
χ322222-2-222-2-22-2-222222-2-2-22-22-222-2-2−2i2i−2i2i0000-22000000000000000000−2i2i−2i2i00000000000000
χ332222-2-222-2-2-1-2-2-1-1-122-211-11-11-1-1112i−2i2i−2i00001-133−3−333−3−30000000000−ii−ii−i3i3−i3i30000000000
χ342222-2-222-2-2-1-2-2-1-1-122-211-11-11-1-1112i−2i2i−2i00001-1−3−333−3−3330000000000−ii−iii3−i3i3−i30000000000
χ352222-2-222-2-2-1-2-2-1-1-122-211-11-11-1-111−2i2i−2i2i00001-133−3−333−3−30000000000i−ii−ii3−i3i3−i30000000000
χ362222-2-222-2-2-1-2-2-1-1-122-211-11-11-1-111−2i2i−2i2i00001-1−3−333−3−3330000000000i−ii−i−i3i3−i3i30000000000
χ372222-2-2-2-222222222-22-2-2-2-22-22-2-22200000000-2200000000222200000000000000-2-200000000
χ382222-2-2-2-222222222-22-2-2-2-22-22-2-22200000000-2200000000-2-2-2-2000000000000002200000000
χ392222-2-2-2-2222-2-22222-22-2-2-22-2222-2-22-2-2200002-20000000000000000002-2-2200000000000000
χ402222-2-2-2-2222-2-22222-22-2-2-22-2222-2-2-222-200002-2000000000000000000-222-200000000000000
χ412222-2-2-2-222-1-2-2-1-1-12-22111-11-1-1-1112-2-220000-1133−3−3−3−3330000000000-111-1−333−30000000000
χ422222-2-2-2-222-1-2-2-1-1-12-22111-11-1-1-1112-2-220000-11−3−33333−3−30000000000-111-13−3−330000000000
χ432222-2-2-2-222-1-2-2-1-1-12-22111-11-1-1-111-222-20000-1133−3−3−3−33300000000001-1-113−3−330000000000
χ442222-2-2-2-222-1-2-2-1-1-12-22111-11-1-1-111-222-20000-11−3−33333−3−300000000001-1-11−333−30000000000
χ4522-2-22-22-22-22002-2-20002-222-2-2000000002−22−2002−22−22−22−200002-22-2000000000000002−22−200
χ4622-2-22-22-22-22002-2-20002-222-2-2000000002−22−2002−22−22−22−20000-22-2200000000000000−22−2200
χ4722-2-22-22-22-22002-2-20002-222-2-200000000−22−2200−22−22−22−2200002-22-200000000000000−22−2200
χ4822-2-22-22-22-22002-2-20002-222-2-200000000−22−2200−22−22−22−220000-22-22000000000000002−22−200
χ4922-2-22-2-22-222002-2-20002-2-2-222000000002−2−22002−22−2−22−2200002i−2i−2i2i00000000000000i2−i2−i2i200
χ5022-2-22-2-22-222002-2-20002-2-2-222000000002−2−22002−22−2−22−220000−2i2i2i−2i00000000000000−i2i2i2−i200
χ5122-2-22-2-22-222002-2-20002-2-2-22200000000−222−200−22−222−22−200002i−2i−2i2i00000000000000−i2i2i2−i200
χ5222-2-22-2-22-222002-2-20002-2-2-22200000000−222−200−22−222−22−20000−2i2i2i−2i00000000000000i2−i2−i2i200
χ534444444444-2-4-4-2-2-2-4-4-4-2-2-2-2-2-222220000000022000000000000000000000000000000000000
χ54444444-4-4-4-4-2-4-4-2-2-2-444-2-22222222200000000-2-2000000000000000000000000000000000000
χ554444-4-444-4-4-244-2-2-2-4-4422-22-2222-2-200000000-22000000000000000000000000000000000000
χ564444-4-4-4-444-244-2-2-2-44-4222-22-222-2-2000000002-2000000000000000000000000000000000000
χ5744-4-44-44-44-4-200-222000-22-2-2220000000022−2222−2200−22−22−22−220000000000000000000000000000
χ5844-4-44-44-44-4-200-222000-22-2-22200000000−2222−2222002−22−22−22−20000000000000000000000000000
χ5944-4-44-4-44-44-200-222000-2222-2-20000000022−22−222200−22−222−22−20000000000000000000000000000
χ6044-4-44-4-44-44-200-222000-2222-2-200000000−222222−22002−22−2−22−220000000000000000000000000000
χ6144-4-4-444-4-444004-4-4000-444-4-4400000000000000000000000000000000000000000000000000
χ6244-4-4-444-4-44-200-2220002-2-222-2000000000000006−6−666−6−660000000000000000000000000000
χ6344-4-4-444-4-44-200-2220002-2-222-200000000000000−666−6−666−60000000000000000000000000000
χ6444-4-4-44-444-44004-4-4000-44-444-400000000000000000000000000000000000000000000000000
χ6544-4-4-44-444-4-200-2220002-22-2-22000000000000006−6−66−666−60000000000000000000000000000
χ6644-4-4-44-444-4-200-2220002-22-2-2200000000000000−666−66−6−660000000000000000000000000000
χ674-44-400000044-4-4-44000000000004-4000000000000000000004i−4i000000000000000000000000
χ684-44-400000044-4-4-44000000000004-400000000000000000000−4i4i000000000000000000000000
χ694-44-40000004-44-4-4400000000000-440000000000000000004i−4i00000000000000000000000000
χ704-44-40000004-44-4-4400000000000-44000000000000000000−4i4i00000000000000000000000000
χ718-88-8000000-48-844-400000000000-440000000000000000000000000000000000000000000000
χ728-88-8000000-4-8844-4000000000004-40000000000000000000000000000000000000000000000
χ738-8-88000000800-88-800000000000000000000000000000000000000000000000000000000000
χ748-8-88000000-4004-4400000000043−43000000000000000000000000000000000000000000000000
χ758-8-88000000-4004-44000000000−4343000000000000000000000000000000000000000000000000

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