Finite Group Databasebeta

← Group #10692045

Character table — Group #10692045

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order122222344444466612121212224444444446612121212121244446612121212121212121212121212121212888888888888888888242424242288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1111-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ611111111111111111111-1-1111-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1
χ711111111111111111111-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ811111111111111111111-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111
χ91111-1-111-1-1-11-1111-1-1-1-11111-111-1-1-1-1-1-11111-1-1ii−i−i111-111-1-1-1-1iiii−i−i−i−iii−i−iii−i−iiiii−i−i−i−ii−iii−i−i1-11-1
χ101111-1-111-1-1-11-1111-1-1-1-11111-111-1-1-1-1-1-11111-1-1ii−i−i111-111-1-1-1-1iiii−i−i−i−i−i−iii−i−iii−i−i−i−iiiiii−iii−i−i-11-11
χ111111-1-111-1-1-11-1111-1-1-1-11111-111-1-1-1-1-1-11111-1-1−i−iii111-111-1-1-1-1−i−i−i−iiiiiii−i−iii−i−iiiii−i−i−i−i−ii−i−iii-11-11
χ121111-1-111-1-1-11-1111-1-1-1-11111-111-1-1-1-1-1-11111-1-1−i−iii111-111-1-1-1-1−i−i−i−iiiii−i−iii−i−iii−i−i−i−iiiii−ii−i−iii1-11-1
χ131111-1-111-1-1-11-1111-1-1-1-1-1-111-1-1-11111-1-11111-1-1ii−i−i-1-11-1-1-11111iiii−i−i−i−iii−i−iii−i−i−i−i−i−iiiii−ii−i−iii-111-1
χ141111-1-111-1-1-11-1111-1-1-1-1-1-111-1-1-11111-1-11111-1-1ii−i−i-1-11-1-1-11111iiii−i−i−i−i−i−iii−i−iiiiiii−i−i−i−i−ii−i−iii1-1-11
χ151111-1-111-1-1-11-1111-1-1-1-1-1-111-1-1-11111-1-11111-1-1−i−iii-1-11-1-1-11111−i−i−i−iiiiiii−i−iii−i−i−i−i−i−iiiiii−iii−i−i1-1-11
χ161111-1-111-1-1-11-1111-1-1-1-1-1-111-1-1-11111-1-11111-1-1−i−iii-1-11-1-1-11111−i−i−i−iiiii−i−iii−i−iiiiiii−i−i−i−ii−iii−i−i-111-1
χ172222222222-22-2222222222-2-2-2-2-222-2-22222-2-2-2-2000022-2-2-2-222-2-20000000000000000000000000000000000
χ182222222222-22-22222222-2-2-2-2-222-2-2222222-2-2-2-20000-2-2-2-222-2-2220000000000000000000000000000000000
χ192222222-2-2-22-22222-2-2-2-2002-2-200000022-2-2-2-2220000002-2000000000000000000000022-2-222-2-20000000000
χ202222222-2-2-22-22222-2-2-2-2002-2-200000022-2-2-2-2220000002-20000000000000000000000-2-222-2-2220000000000
χ212222222-2-2-2-2-2-2222-2-2-2-200-22200000022-2-222-2-2000000-22000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ222222222-2-2-2-2-2-2222-2-2-2-200-22200000022-2-222-2-2000000-2200000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ23222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ24222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ25222222-1222222-1-1-1-1-1-1-1-2-2222-2-2-2-2-2-2-1-1-1-1-1-1-1-1222211-1-1111111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ26222222-1222222-1-1-1-1-1-1-1-2-2222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-211-1-111111111111111000000000000000022-1-1-1-10000
χ27222222-1222-22-2-1-1-1-1-1-1-122-2-2-2-2-222-2-2-1-1-1-111110000-1-11111-1-111−i3−i3i3i3−i3−i3i3i3000000000000000000−i3i3−i3i30000
χ28222222-1222-22-2-1-1-1-1-1-1-122-2-2-2-2-222-2-2-1-1-1-111110000-1-11111-1-111i3i3−i3−i3i3i3−i3−i3000000000000000000i3−i3i3−i30000
χ29222222-1222-22-2-1-1-1-1-1-1-1-2-2-2-2-222-2-222-1-1-1-1111100001111-1-111-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000i3−i3i3−i30000
χ30222222-1222-22-2-1-1-1-1-1-1-1-2-2-2-2-222-2-222-1-1-1-1111100001111-1-111-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000−i3i3−i3i30000
χ312222-2-222-2-2222222-2-2-2-222-2-22-2-2-2-222-2-222-2-222000022-22-2-2-2-2220000000000000000000000000000000000
χ322222-2-222-2-2222222-2-2-2-2-2-2-2-222222-2-2-2-222-2-2220000-2-2-222222-2-20000000000000000000000000000000000
χ332222-2-22-2222-22222222200-22-2000000-2-2-2-22222000000-2-2000000000000002222-2-2-2-2000000000000000000
χ342222-2-22-2222-22222222200-22-2000000-2-2-2-22222000000-2-200000000000000-2-2-2-22222000000000000000000
χ352222-2-22-222-2-2-22222222002-22000000-2-2-2-2-2-2-2-20000002200000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ362222-2-22-222-2-2-22222222002-22000000-2-2-2-2-2-2-2-2000000220000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ372222-2-2-12-2-2222-1-1-1111122-2-22-2-2-2-22211-1-111-1-10000-1-11-11111-1-133−3−3−3−3330000000000000000003−3−330000
χ382222-2-2-12-2-2222-1-1-1111122-2-22-2-2-2-22211-1-111-1-10000-1-11-11111-1-1−3−33333−3−3000000000000000000−333−30000
χ392222-2-2-12-2-2222-1-1-11111-2-2-2-222222-2-211-1-111-1-10000111-1-1-1-1-11133−3−3−3−333000000000000000000−333−30000
χ402222-2-2-12-2-2222-1-1-11111-2-2-2-222222-2-211-1-111-1-10000111-1-1-1-1-111−3−33333−3−30000000000000000003−3−330000
χ412222-2-2-12-2-2-22-2-1-1-111112222-222-2-2-2-211-1-1-1-1112i2i−2i−2i-1-1-11-1-11111−i−i−i−iiiii00000000000000002i−2i−i−iii0000
χ422222-2-2-12-2-2-22-2-1-1-111112222-222-2-2-2-211-1-1-1-111−2i−2i2i2i-1-1-11-1-11111iiii−i−i−i−i0000000000000000−2i2iii−i−i0000
χ432222-2-2-12-2-2-22-2-1-1-11111-2-222-2-2-2222211-1-1-1-1112i2i−2i−2i11-1111-1-1-1-1−i−i−i−iiiii0000000000000000−2i2iii−i−i0000
χ442222-2-2-12-2-2-22-2-1-1-11111-2-222-2-2-2222211-1-1-1-111−2i−2i2i2i11-1111-1-1-1-1iiii−i−i−i−i00000000000000002i−2i−i−iii0000
χ4522-2-22-222-220-202-2-2-2-222000002i−2i002i−2i2-22-20000000000002i−2i002i−2i000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000
χ4622-2-22-222-220-202-2-2-2-222000002i−2i002i−2i2-22-20000000000002i−2i002i−2i00000000−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000
χ4722-2-22-222-220-202-2-2-2-22200000−2i2i00−2i2i2-22-2000000000000−2i2i00−2i2i000000002−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000
χ4822-2-22-222-220-202-2-2-2-22200000−2i2i00−2i2i2-22-2000000000000−2i2i00−2i2i00000000−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000
χ4922-2-22-22-22-20202-2-222-2-22-2000002-2002-2-22000000002-200002-20000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000
χ5022-2-22-22-22-20202-2-222-2-22-2000002-2002-2-22000000002-200002-20000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000
χ5122-2-22-22-22-20202-2-222-2-2-2200000-22002-2-2200000000-220000-220000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000
χ5222-2-22-22-22-20202-2-222-2-2-2200000-22002-2-2200000000-220000-220000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000
χ5322-2-2-22222-20-202-2-222-2-2000002i−2i00−2i2i-222-20000000000002i−2i00−2i2i00000000−i2i2i2−i2−i2i2i2−i2−22−222−22−20000000000
χ5422-2-2-22222-20-202-2-222-2-2000002i−2i00−2i2i-222-20000000000002i−2i00−2i2i00000000i2−i2−i2i2i2−i2−i2i22−22−2−22−220000000000
χ5522-2-2-22222-20-202-2-222-2-200000−2i2i002i−2i-222-2000000000000−2i2i002i−2i00000000−i2i2i2−i2−i2i2i2−i22−22−2−22−220000000000
χ5622-2-2-22222-20-202-2-222-2-200000−2i2i002i−2i-222-2000000000000−2i2i002i−2i00000000i2−i2−i2i2i2−i2−i2i2−22−222−22−20000000000
χ5722-2-2-222-2-220202-2-2-2-2222-200000-2200-22-22000000002-20000-2200000000002−22−2−22−222−2−22−222−20000000000
χ5822-2-2-222-2-220202-2-2-2-2222-200000-2200-22-22000000002-20000-220000000000−22−222−22−2−222−22−2−220000000000
χ5922-2-2-222-2-220202-2-2-2-222-22000002-200-22-2200000000-2200002-200000000002−22−2−22−22−222−22−2−220000000000
χ6022-2-2-222-2-220202-2-2-2-222-22000002-200-22-2200000000-2200002-20000000000−22−222−22−22−2−22−222−20000000000
χ61444444-2-4-4-44-44-2-2-22222004-4-4000000-2-22222-2-2000000-220000000000000000000000000000000000000000
χ62444444-2-4-4-4-4-4-4-2-2-2222200-444000000-2-222-2-2220000002-20000000000000000000000000000000000000000
χ634444-4-4-2-4444-44-2-2-2-2-2-2-200-44-40000002222-2-2-2-2000000220000000000000000000000000000000000000000
χ644444-4-4-2-444-4-4-4-2-2-2-2-2-2-2004-4400000022222222000000-2-20000000000000000000000000000000000000000
χ6544-4-44-4-24-440-40-22222-2-2000004i−4i004i−4i-22-22000000000000−2i2i00−2i2i0000000000000000000000000000000000
χ6644-4-44-4-24-440-40-22222-2-200000−4i4i00−4i4i-22-220000000000002i−2i002i−2i0000000000000000000000000000000000
χ6744-4-44-4-2-44-4040-222-2-2224-4000004-400-222-200000000-220000-22000000000000000000000000000000000000
χ6844-4-44-4-2-44-4040-222-2-222-4400000-4400-222-2000000002-200002-2000000000000000000000000000000000000
χ6944-4-4-44-244-40-40-222-2-222000004i−4i00−4i4i2-2-22000000000000−2i2i002i−2i0000000000000000000000000000000000
χ7044-4-4-44-244-40-40-222-2-22200000−4i4i004i−4i2-2-220000000000002i−2i00−2i2i0000000000000000000000000000000000
χ7144-4-4-44-2-4-44040-22222-2-24-400000-44002-22-200000000-2200002-2000000000000000000000000000000000000
χ7244-4-4-44-2-4-44040-22222-2-2-44000004-4002-22-2000000002-20000-22000000000000000000000000000000000000
χ734-44-400400040-4-44-40000000000000000000004-42i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ744-44-400400040-4-44-40000000000000000000004-4−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ754-44-4004000-404-44-4000000000000000000000-442-2-2200000000002-22-2-22-2200000000000000000000000000
χ764-44-4004000-404-44-4000000000000000000000-44-222-20000000000-22-222-22-200000000000000000000000000
χ774-44-400-200040-42-2223−2323−2300000000000000023−23-222i−2i2i−2i0000000000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ2200000000000000000000000000
χ784-44-400-200040-42-2223−2323−2300000000000000023−23-22−2i2i−2i2i0000000000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ2200000000000000000000000000
χ794-44-400-200040-42-22−2323−2323000000000000000−2323-222i−2i2i−2i0000000000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ2200000000000000000000000000
χ804-44-400-200040-42-22−2323−2323000000000000000−2323-22−2i2i−2i2i0000000000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ2200000000000000000000000000
χ814-44-400-2000-4042-2223−2323−23000000000000000−23232-22-2-220000000000−1+31−3−1−31+31+3−1−31−3−1+300000000000000000000000000
χ824-44-400-2000-4042-2223−2323−23000000000000000−23232-2-222-200000000001−3−1+31+3−1−3−1−31+3−1+31−300000000000000000000000000
χ834-44-400-2000-4042-22−2323−232300000000000000023−232-22-2-220000000000−1−31+3−1+31−31−3−1+31+3−1−300000000000000000000000000
χ844-44-400-2000-4042-22−2323−232300000000000000023−232-2-222-200000000001+3−1−31−3−1+3−1+31−3−1−31+300000000000000000000000000
χ858-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000000
χ878-8-8800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000000

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