Finite Group Databasebeta

← Group #10705479

Character table — Group #10705479

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order1222223444466612121212224444446666661212121212124444444444121212121212121212121212121212121212121212121212888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ7111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1
χ91111111-1-1-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-11-1
χ101111111-1-1-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-11-11
χ111111111-1-1-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11-11
χ121111111-1-1-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-11-1
χ131111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-1ii−i−i−i−iii11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-1ii−i−i−i−iii11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-1−i−iiiii−i−i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-1−i−iiiii−i−i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ172222222222222222222222-2-2-2-2222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-2222222-2-2-2-222-2-2-2-2-2-200000000-2-2-2-222220000000000000000000000000000
χ192222222-2-2-2-2222-2-2-2-222-2-222-2-2222222-2-2-2-2-2-2-2200000000-2-222-2-2220000000000000000000000000000
χ202222222-2-2-2-2222-2-2-2-2-2-222-2-22222-2-2-2-2-2-22222-2200000000-2-22222-2-20000000000000000000000000000
χ21222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000
χ23222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ24222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-11111-1-11111-2-2000000001111-1-1-1-133−3−333−3−3−3−333−3−333000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-11111-1-11111-2-2000000001111-1-1-1-1−3−333−3−33333−3−333−3−3000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-11111222i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1111122−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i000000000000
χ29222222-1-2-2-2-2-1-1-1111122-2-222-2-2-1-1-1-1-1-1111111-220000000011-1-111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3000000000000
χ30222222-1-2-2-2-2-1-1-1111122-2-222-2-2-1-1-1-1-1-1111111-220000000011-1-111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3000000000000
χ31222222-1-2-2-2-2-1-1-1111122-2-2-2-222-1-1-1-1-1-11111112-222-2-222-2-2-1-111-1-111-1-1-1-11111-1-1-1-11111000000000000
χ32222222-1-2-2-2-2-1-1-1111122-2-2-2-222-1-1-1-1-1-11111112-2-2-222-2-222-1-111-1-1111111-1-1-1-11111-1-1-1-1000000000000
χ33222222-1-2-2-2-2-1-1-11111-2-22222-2-2-1-1111111-1-1-1-12-22i2i−2i−2i−2i−2i2i2i-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ34222222-1-2-2-2-2-1-1-11111-2-22222-2-2-1-1111111-1-1-1-12-2−2i−2i2i2i2i2i−2i−2i-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000
χ35222222-1-2-2-2-2-1-1-11111-2-222-2-222-1-1111111-1-1-1-1-220000000011-1-1-1-11133−3−3−3−333−3−33333−3−3000000000000
χ36222222-1-2-2-2-2-1-1-11111-2-222-2-222-1-1111111-1-1-1-1-220000000011-1-1-1-111−3−33333−3−333−3−3−3−333000000000000
χ3722-2-22-2222-2-22-2-222-2-22-22-200002-222-2-22-222-2-200000000000000000000000000000000002−22−22−22−20000
χ3822-2-22-2222-2-22-2-222-2-22-22-200002-222-2-22-222-2-20000000000000000000000000000000000−22−22−22−220000
χ3922-2-22-2222-2-22-2-222-2-2-22-2200002-2-2-2222-2-2-2220000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ4022-2-22-2222-2-22-2-222-2-2-22-2200002-2-2-2222-2-2-2220000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ4122-2-22-22-2-2222-2-2-2-2222-2-2200002-222-2-2-22-2-22200000000000000000000000000000000002−2−222−2−220000
χ4222-2-22-22-2-2222-2-2-2-2222-2-2200002-222-2-2-22-2-2220000000000000000000000000000000000−222−2−222−20000
χ4322-2-22-22-2-2222-2-2-2-222-222-200002-2-2-222-2222-2-20000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ4422-2-22-22-2-2222-2-2-2-222-222-200002-2-2-222-2222-2-20000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ4522-2-2-2222-22-22-2-222-2-200002i−2i2i−2i-220000-220000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00002i−2i2i−2i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i000000000000
χ4622-2-2-2222-22-22-2-222-2-200002i−2i2i−2i-220000-22000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002i−2i2i−2i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i000000000000
χ4722-2-2-2222-22-22-2-222-2-20000−2i2i−2i2i-220000-220000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000−2i2i−2i2i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i000000000000
χ4822-2-2-2222-22-22-2-222-2-20000−2i2i−2i2i-220000-22000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000−2i2i−2i2i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i000000000000
χ4922-2-2-222-22-222-2-2-2-22200002i−2i−2i2i-2200002-20000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000−2i2i2i−2i1−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i000000000000
χ5022-2-2-222-22-222-2-2-2-22200002i−2i−2i2i-2200002-2000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000−2i2i2i−2i−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i000000000000
χ5122-2-2-222-22-222-2-2-2-2220000−2i2i2i−2i-2200002-20000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00002i−2i−2i2i1+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i000000000000
χ5222-2-2-222-22-222-2-2-2-2220000−2i2i2i−2i-2200002-2000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00002i−2i−2i2i−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i000000000000
χ5322-2-2-22-12-22-2-111-1-11100002i−2i2i−2i1-1−i3i3−i3i31-1−i3i3−i3i3001+i−1−i1+i−1−i1−i−1+i1−i−1+i3−33−3−ii−ii−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22000000000000
χ5422-2-2-22-12-22-2-111-1-11100002i−2i2i−2i1-1−i3i3−i3i31-1−i3i3−i3i300−1−i1+i−1−i1+i−1+i1−i−1+i1−i3−33−3−ii−iiζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22000000000000
χ5522-2-2-22-12-22-2-111-1-11100002i−2i2i−2i1-1i3−i3i3−i31-1i3−i3i3−i3001+i−1−i1+i−1−i1−i−1+i1−i−1+i−33−33−ii−ii−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14000000000000
χ5622-2-2-22-12-22-2-111-1-11100002i−2i2i−2i1-1i3−i3i3−i31-1i3−i3i3−i300−1−i1+i−1−i1+i−1+i1−i−1+i1−i−33−33−ii−iiζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14000000000000
χ5722-2-2-22-12-22-2-111-1-1110000−2i2i−2i2i1-1−i3i3−i3i31-1−i3i3−i3i3001−i−1+i1−i−1+i1+i−1−i1+i−1−i−33−33i−ii−i−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000000000
χ5822-2-2-22-12-22-2-111-1-1110000−2i2i−2i2i1-1−i3i3−i3i31-1−i3i3−i3i300−1+i1−i−1+i1−i−1−i1+i−1−i1+i−33−33i−ii−iζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000000000
χ5922-2-2-22-12-22-2-111-1-1110000−2i2i−2i2i1-1i3−i3i3−i31-1i3−i3i3−i3001−i−1+i1−i−1+i1+i−1−i1+i−1−i3−33−3i−ii−i−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14000000000000
χ6022-2-2-22-12-22-2-111-1-1110000−2i2i−2i2i1-1i3−i3i3−i31-1i3−i3i3−i300−1+i1−i−1+i1−i−1−i1+i−1−i1+i3−33−3i−ii−iζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000000000
χ6122-2-2-22-1-22-22-11111-1-100002i−2i−2i2i1-1−i3i3−i3i3-11i3−i3i3−i3001−i−1+i−1+i1−i1+i−1−i−1−i1+i−333−3i−i−ii−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000000000
χ6222-2-2-22-1-22-22-11111-1-100002i−2i−2i2i1-1−i3i3−i3i3-11i3−i3i3−i300−1+i1−i1−i−1+i−1−i1+i1+i−1−i−333−3i−i−iiζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000000000
χ6322-2-2-22-1-22-22-11111-1-100002i−2i−2i2i1-1i3−i3i3−i3-11−i3i3−i3i3001−i−1+i−1+i1−i1+i−1−i−1−i1+i3−3−33i−i−ii−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000000000
χ6422-2-2-22-1-22-22-11111-1-100002i−2i−2i2i1-1i3−i3i3−i3-11−i3i3−i3i300−1+i1−i1−i−1+i−1−i1+i1+i−1−i3−3−33i−i−iiζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14000000000000
χ6522-2-2-22-1-22-22-11111-1-10000−2i2i2i−2i1-1−i3i3−i3i3-11i3−i3i3−i3001+i−1−i−1−i1+i1−i−1+i−1+i1−i3−3−33−iii−i−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22000000000000
χ6622-2-2-22-1-22-22-11111-1-10000−2i2i2i−2i1-1−i3i3−i3i3-11i3−i3i3−i300−1−i1+i1+i−1−i−1+i1−i1−i−1+i3−3−33−iii−iζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22000000000000
χ6722-2-2-22-1-22-22-11111-1-10000−2i2i2i−2i1-1i3−i3i3−i3-11−i3i3−i3i3001+i−1−i−1−i1+i1−i−1+i−1+i1−i−333−3−iii−i−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14000000000000
χ6822-2-2-22-1-22-22-11111-1-10000−2i2i2i−2i1-1i3−i3i3−i3-11−i3i3−i3i300−1−i1+i1+i−1−i−1+i1−i1−i−1+i−333−3−iii−iζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14000000000000
χ694444-4-444-4-44444444400000000-4-40000-4-400000000000000000000000000000000000000000000000000
χ704444-4-44-444-4444-4-4-4-400000000-4-400004400000000000000000000000000000000000000000000000000
χ714444-4-4-24-4-44-2-2-2-2-2-2-20000000022−2i32i32i3−2i322−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ724444-4-4-24-4-44-2-2-2-2-2-2-200000000222i3−2i3−2i32i3222i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ734444-4-4-2-444-4-2-2-222220000000022−2i32i32i3−2i3-2-22i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ744444-4-4-2-444-4-2-2-2222200000000222i3−2i3−2i32i3-2-2−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ7544-4-44-4-244-4-4-222-2-2224-44-40000-22-2-222-22-2-2220000000000000000000000000000000000000000000000
χ7644-4-44-4-244-4-4-222-2-222-44-440000-2222-2-2-2222-2-20000000000000000000000000000000000000000000000
χ7744-4-44-4-2-4-444-22222-2-24-4-440000-22-2-2222-222-2-20000000000000000000000000000000000000000000000
χ7844-4-44-4-2-4-444-22222-2-2-444-40000-2222-2-22-2-2-2220000000000000000000000000000000000000000000000
χ798-88-80080000-88-80000000000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-400004-4443−4343−43000000000000000000000000000000000000000000000000000000000000000000
χ818-88-800-400004-44−4343−4343000000000000000000000000000000000000000000000000000000000000000000
χ828-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ838-8-8800-4000044-443−43−4343000000000000000000000000000000000000000000000000000000000000000000
χ848-8-8800-4000044-4−434343−43000000000000000000000000000000000000000000000000000000000000000000

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