Finite Group Databasebeta

← Group #10692041

Character table — Group #10692041

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order12222234444446661212121244466888888881212121212124444121212121212121212122424242424242424224444448888888888242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1
χ71111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ81111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111
χ91111-1-111-1-11-1-111111111-11-1-1ii−i−iii−i−i-1-1-1-1-1-1ii−i−i11iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-111-1-11-1i−i
χ101111-1-111-1-11-1-111111111-11-1-1ii−i−iii−i−i-1-1-1-1-1-1ii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-111-1-1-11−ii
χ111111-1-111-1-11-1-111111111-11-1-1ii−i−iii−i−i-1-1-1-1-1-1−i−iii11−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11-1-111-11−ii
χ121111-1-111-1-11-1-111111111-11-1-1ii−i−iii−i−i-1-1-1-1-1-1−i−iii11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11-1-1111-1i−i
χ131111-1-111-1-11-1-111111111-11-1-1−i−iii−i−iii-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11-1-111-11i−i
χ141111-1-111-1-11-1-111111111-11-1-1−i−iii−i−iii-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11-1-1111-1−ii
χ151111-1-111-1-11-1-111111111-11-1-1−i−iii−i−iii-1-1-1-1-1-1−i−iii11−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-111-1-11-1−ii
χ161111-1-111-1-11-1-111111111-11-1-1−i−iii−i−iii-1-1-1-1-1-1−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-111-1-1-11i−i
χ17222222222-222-22222222-2-2-2220000000022-2-2-2-20000-2-2000000000000000022-2-222-2-2000000000000000000
χ18222222222-222-22222222-2-2-2220000000022-2-2-2-20000-2-20000000000000000-2-222-2-222000000000000000000
χ192222222-2-22-2-22222-2-2-2-2-2-222200000000-2-2-2-22200002-200000000000000000000000022-2-222-2-20000000000
χ202222222-2-22-2-22222-2-2-2-2-2-222200000000-2-2-2-22200002-2000000000000000000000000-2-222-2-2220000000000
χ212222222-2-2-2-2-2-2222-2-2-2-222-2222i2i−2i−2i−2i−2i2i2i-2-222-2-20000-22000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ222222222-2-2-2-2-2-2222-2-2-2-222-222−2i−2i2i2i2i2i−2i−2i-2-222-2-20000-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-122222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ24222222-1222222-1-1-1-1-1-1-1222-1-122222222-1-1-1-1-1-1-2-2-2-2-1-111111111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ25222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ26222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-2-2-2-2-1-11111111111111111000000000000000022-1-1-1-10000
χ27222222-1-2-2-2-2-2-2-1-1-1111122-2-1-12i2i−2i−2i−2i−2i2i2i11-1-11100001-1−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii0000000000000000003−33−30000
χ28222222-1-2-2-2-2-2-2-1-1-1111122-2-1-12i2i−2i−2i−2i−2i2i2i11-1-11100001-1i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii000000000000000000−33−330000
χ29222222-1-2-2-2-2-2-2-1-1-1111122-2-1-1−2i−2i2i2i2i2i−2i−2i11-1-11100001-1−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i000000000000000000−33−330000
χ30222222-1-2-2-2-2-2-2-1-1-1111122-2-1-1−2i−2i2i2i2i2i−2i−2i11-1-11100001-1i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i0000000000000000003−33−30000
χ312222-2-222-222-222222222-22-2-2-200000000-2-222220000-2-2000000000000000022-2-2-2-222000000000000000000
χ322222-2-222-222-222222222-22-2-2-200000000-2-222220000-2-20000000000000000-2-22222-2-2000000000000000000
χ332222-2-22-222-222222-2-2-2-22-2-2-2-22222-2-2-2-222-2-2220000-220000000022-2-2-2-22200000000000000000000000000
χ342222-2-22-222-222222-2-2-2-22-2-2-2-2-2-2-2-2222222-2-2220000-2200000000-2-22222-2-200000000000000000000000000
χ352222-2-22-22-2-22-2222-2-2-2-2-222-2-2000000002222-2-200002-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ362222-2-22-22-2-22-2222-2-2-2-2-222-2-2000000002222-2-200002-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ372222-2-2-12-2-22-2-2-1-1-1-1-1-1-12-22112i2i−2i−2i2i2i−2i−2i1111112i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii00000000000000002-2-1-1110000
χ382222-2-2-12-2-22-2-2-1-1-1-1-1-1-12-22112i2i−2i−2i2i2i−2i−2i111111−2i−2i2i2i-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000-2211-1-10000
χ392222-2-2-12-2-22-2-2-1-1-1-1-1-1-12-2211−2i−2i2i2i−2i−2i2i2i1111112i2i−2i−2i-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000-2211-1-10000
χ402222-2-2-12-2-22-2-2-1-1-1-1-1-1-12-2211−2i−2i2i2i−2i−2i2i2i111111−2i−2i2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i00000000000000002-2-1-1110000
χ412222-2-2-1-222-222-1-1-111112-2-2112222-2-2-2-2-1-111-1-100001-133−3−3−3−333-1-11111-1-1000000000000000000−333−30000
χ422222-2-2-1-222-222-1-1-111112-2-2112222-2-2-2-2-1-111-1-100001-1−3−33333−3−3-1-11111-1-10000000000000000003−3−330000
χ432222-2-2-1-222-222-1-1-111112-2-211-2-2-2-22222-1-111-1-100001-133−3−3−3−33311-1-1-1-1110000000000000000003−3−330000
χ442222-2-2-1-222-222-1-1-111112-2-211-2-2-2-22222-1-111-1-100001-1−3−33333−3−311-1-1-1-111000000000000000000−333−30000
χ4522-2-22-22220-2-202-2-222-2-20002-22−22−22−22−22-20000000000000000002−22−22−22−22-2002-2002−22−22−22−20000000000
χ4622-2-22-22220-2-202-2-222-2-20002-22−22−22−22−22-20000000000000000002−22−22−22−2-2200-2200−22−22−22−220000000000
χ4722-2-22-22220-2-202-2-222-2-20002-2−22−22−22−222-2000000000000000000−22−22−22−222-2002-200−22−22−22−220000000000
χ4822-2-22-22220-2-202-2-222-2-20002-2−22−22−22−222-2000000000000000000−22−22−22−22-2200-22002−22−22−22−20000000000
χ4922-2-22-22-2-202202-2-2-2-2220002-2−i2i2i2−i2i2−i2−i2i2-22000000000000000000−i2i2i2−i2−i2i2i2−i2002i−2i002i−2i2−2−222−2−220000000000
χ5022-2-22-22-2-202202-2-2-2-2220002-2−i2i2i2−i2i2−i2−i2i2-22000000000000000000−i2i2i2−i2−i2i2i2−i200−2i2i00−2i2i−222−2−222−20000000000
χ5122-2-22-22-2-202202-2-2-2-2220002-2i2−i2−i2i2−i2i2i2−i2-22000000000000000000i2−i2−i2i2i2−i2−i2i2002i−2i002i−2i−222−2−222−20000000000
χ5222-2-22-22-2-202202-2-2-2-2220002-2i2−i2−i2i2−i2i2i2−i2-22000000000000000000i2−i2−i2i2i2−i2−i2i200−2i2i00−2i2i2−2−222−2−220000000000
χ5322-2-2-2222-20-2202-2-222-2-2000-22−i2i2i2−i2−i2i2i2−i2-22000000000000000000−i2i2−i2i2i2−i2i2−i22-200-2200−i2i2−i2i2i2−i2i2−i20000000000
χ5422-2-2-2222-20-2202-2-222-2-2000-22−i2i2i2−i2−i2i2i2−i2-22000000000000000000−i2i2−i2i2i2−i2i2−i2-22002-200i2−i2i2−i2−i2i2−i2i20000000000
χ5522-2-2-2222-20-2202-2-222-2-2000-22i2−i2−i2i2i2−i2−i2i2-22000000000000000000i2−i2i2−i2−i2i2−i2i22-200-2200i2−i2i2−i2−i2i2−i2i20000000000
χ5622-2-2-2222-20-2202-2-222-2-2000-22i2−i2−i2i2i2−i2−i2i2-22000000000000000000i2−i2i2−i2−i2i2−i2i2-22002-200−i2i2−i2i2i2−i2i2−i20000000000
χ5722-2-2-222-2202-202-2-2-2-222000-222−22−2−22−222-20000000000000000002−2−22−222−2002i−2i00−2i2ii2−i2−i2i2−i2i2i2−i20000000000
χ5822-2-2-222-2202-202-2-2-2-222000-222−22−2−22−222-20000000000000000002−2−22−222−200−2i2i002i−2i−i2i2i2−i2i2−i2−i2i20000000000
χ5922-2-2-222-2202-202-2-2-2-222000-22−22−222−22−22-2000000000000000000−222−22−2−22002i−2i00−2i2i−i2i2i2−i2i2−i2−i2i20000000000
χ6022-2-2-222-2202-202-2-2-2-222000-22−22−222−22−22-2000000000000000000−222−22−2−2200−2i2i002i−2ii2−i2−i2i2−i2i2i2−i20000000000
χ61444444-244-444-4-2-2-2-2-2-2-2-4-4-4-2-200000000-2-22222000022000000000000000000000000000000000000000000
χ62444444-2-4-44-4-44-2-2-22222-4-44-2-2000000002222-2-20000-22000000000000000000000000000000000000000000
χ634444-4-4-24-444-44-2-2-2-2-2-2-2-44-4220000000022-2-2-2-2000022000000000000000000000000000000000000000000
χ644444-4-4-2-44-4-44-4-2-2-22222-4442200000000-2-2-2-2220000-22000000000000000000000000000000000000000000
χ6544-4-44-4-2440-4-40-222-2-222000-2222−2222−2222−2222−22-22000000000000000000−22−22−22−2200000000000000000000000000
χ6644-4-44-4-2440-4-40-222-2-222000-22−2222−2222−2222−2222-220000000000000000002−22−22−22−200000000000000000000000000
χ6744-4-44-4-2-4-40440-22222-2-2000-22−2i22i22i2−2i22i2−2i2−2i22i22-2000000000000000000i2−i2−i2i2i2−i2−i2i200000000000000000000000000
χ6844-4-44-4-2-4-40440-22222-2-2000-222i2−2i2−2i22i2−2i22i22i2−2i22-2000000000000000000−i2i2i2−i2−i2i2i2−i200000000000000000000000000
χ6944-4-4-44-24-40-440-222-2-2220002-2−2i22i22i2−2i2−2i22i22i2−2i22-2000000000000000000i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ7044-4-4-44-24-40-440-222-2-2220002-22i2−2i2−2i22i22i2−2i2−2i22i22-2000000000000000000−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ7144-4-4-44-2-4404-40-22222-2-20002-222−2222−22−2222−2222-22000000000000000000−222−22−2−2200000000000000000000000000
χ7244-4-4-44-2-4404-40-22222-2-20002-2−2222−222222−2222−22-220000000000000000002−2−22−222−200000000000000000000000000
χ734-4-4400400400-4-44-40000000000000000000004-42i−2i2i−2i002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000
χ744-4-4400400400-4-44-40000000000000000000004-4−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000
χ754-4-4400400-4004-44-4000000000000000000000-442-2-22002-22-2-22-220000000000000000000000000000000000
χ764-4-4400400-4004-44-4000000000000000000000-44-222-200-22-222-22-20000000000000000000000000000000000
χ774-4-4400-200400-42-2223−2323−2300000000000000023−23-222i−2i2i−2i00−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−ζ220000000000000000000000000000000000
χ784-4-4400-200400-42-2223−2323−2300000000000000023−23-22−2i2i−2i2i00ζ4−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+ζ220000000000000000000000000000000000
χ794-4-4400-200400-42-22−2323−2323000000000000000−2323-222i−2i2i−2i00ζ4+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−ζ220000000000000000000000000000000000
χ804-4-4400-200400-42-22−2323−2323000000000000000−2323-22−2i2i−2i2i00−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+ζ220000000000000000000000000000000000
χ814-4-4400-200-40042-2223−2323−23000000000000000−23232-22-2-2200−1−31+3−1+31−31−3−1+31+3−1−30000000000000000000000000000000000
χ824-4-4400-200-40042-2223−2323−23000000000000000−23232-2-222-2001+3−1−31−3−1+3−1+31−3−1−31+30000000000000000000000000000000000
χ834-4-4400-200-40042-22−2323−232300000000000000023−232-22-2-2200−1+31−3−1−31+31+3−1−31−3−1+30000000000000000000000000000000000
χ844-4-4400-200-40042-22−2323−232300000000000000023−232-2-222-2001−3−1+31+3−1−3−1−31+3−1+31−30000000000000000000000000000000000
χ858-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000000
χ878-88-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000000

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