Finite Group Databasebeta

← Group #10683603

Character table — Group #10683603

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order122222223444444446666666448888888812121212121212124444444488881212242424242424242424242424242424244444888888884412121212888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ9111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i11iiii−i−i−i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i1-1-1-111ii−i−i1-1
χ10111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii11iiii−i−i−i−i−i−i−i−iiiii11-1-1iiii−i−i−i−i-1111-1-1−i−iii-11
χ11111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-111−i−i−i−iiiii1-1-1-111−i−iii-11
χ12111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii11iiii−i−i−i−i−i−i−i−iiiii-1-111−i−i−i−iiiii-1111-1-1ii−i−i1-1
χ13111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i11−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−i−i−iiiii-1111-1-1ii−i−i-11
χ14111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii11−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−i−i−iiiii1-1-1-111−i−iii1-1
χ15111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i11−i−i−i−iiiiiiiii−i−i−i−i-1-111iiii−i−i−i−i-1111-1-1−i−iii1-1
χ16111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-111iiii−i−i−i−i1-1-1-111ii−i−i-11
χ1722222222222-2-2-2-2222222222-2-20000000022-2-222-2-2222222220000-2-20000000000000000-2-2-2-200000000000000000000
χ1822222222222-2-2-2-2222222222-2-20000000022-2-222-2-2-2-2-2-2-2-2-2-20000-2-20000000000000000222200000000000000000000
χ19222222222-2-22222-2-22222222-2-200000000-2-222-2-2222222-2-2-2-20000-2-20000000000000000-2-22200000000000000000000
χ20222222222-2-22222-2-22222222-2-200000000-2-222-2-222-2-2-2-222220000-2-2000000000000000022-2-200000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000002222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ2522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222i2i2i2i−2i−2i−2i−2i11111111000000002i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii0000000000002-211-1-1000000
χ2622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222i2i2i2i−2i−2i−2i−2i1111111100000000−2i−2i2i2i-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000-22-1-111000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122−2i−2i−2i−2i2i2i2i2i11111111000000002i2i−2i−2i-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000-22-1-111000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122−2i−2i−2i−2i2i2i2i2i1111111100000000−2i−2i2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i0000000000002-211-1-1000000
χ292222-2-2-2-22220000-2-222-22-2-2-200000000002200-2-20022-2-222-2-22−22−2000000000022−2−222−2−20000000000000000002−22−200
χ302222-2-2-2-22220000-2-222-22-2-2-200000000002200-2-20022-2-222-2-2−22−220000000000−2−222−2−222000000000000000000−22−2200
χ312222-2-2-2-22220000-2-222-22-2-2-200000000002200-2-200-2-222-2-2222−22−2000000000022−2−222−2−2000000000000000000−22−2200
χ322222-2-2-2-22220000-2-222-22-2-2-200000000002200-2-200-2-222-2-222−22−220000000000−2−222−2−2220000000000000000002−22−200
χ332222-2-2-2-22-2-200002222-22-2-2-20000000000-2-200220022-2-2-2-222−i2i2i2−i20000000000−i2−i2i2i2i2i2−i2−i2000000000000000000−i2i2i2−i200
χ342222-2-2-2-22-2-200002222-22-2-2-20000000000-2-200220022-2-2-2-222i2−i2−i2i20000000000i2i2−i2−i2−i2−i2i2i2000000000000000000i2−i2−i2i200
χ352222-2-2-2-22-2-200002222-22-2-2-20000000000-2-2002200-2-22222-2-2−i2i2i2−i20000000000−i2−i2i2i2i2i2−i2−i2000000000000000000i2−i2−i2i200
χ362222-2-2-2-22-2-200002222-22-2-2-20000000000-2-2002200-2-22222-2-2i2−i2−i2i20000000000i2i2−i2−i2−i2−i2i2i2000000000000000000−i2i2i2−i200
χ3722-2-2-22-222002i−2i2i−2i00-2-222-22-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i002i−2i002i−2i00002i−2i2i−2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000002-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ3822-2-2-22-222002i−2i2i−2i00-2-222-22-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i002i−2i002i−2i0000−2i2i−2i2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000-2200−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ3922-2-2-22-222002i−2i2i−2i00-2-222-22-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i002i−2i002i−2i00002i−2i2i−2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000002-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ4022-2-2-22-222002i−2i2i−2i00-2-222-22-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i002i−2i002i−2i0000−2i2i−2i2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000-22001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ4122-2-2-22-22200−2i2i−2i2i00-2-222-22-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i00−2i2i00−2i2i00002i−2i2i−2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000-2200−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ4222-2-2-22-22200−2i2i−2i2i00-2-222-22-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i00−2i2i00−2i2i0000−2i2i−2i2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000002-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ4322-2-2-22-22200−2i2i−2i2i00-2-222-22-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−2i2i00−2i2i00002i−2i2i−2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000-22001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ4422-2-2-22-22200−2i2i−2i2i00-2-222-22-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−2i2i00−2i2i0000−2i2i−2i2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000002-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ452-22-222-2-220022-2-2002-2-2-2-222002−22−22−22−200-2-200222i−2i2i−2i00000000002−22−22−22−200000000002i−2i−i2i2−i2i2−i2i2−i2i2000000000000
χ462-22-222-2-220022-2-2002-2-2-2-222002−22−22−22−200-2-20022−2i2i−2i2i00000000002−22−22−22−20000000000−2i2ii2−i2i2−i2i2−i2i2−i2000000000000
χ472-22-222-2-220022-2-2002-2-2-2-22200−22−22−22−2200-2-200222i−2i2i−2i0000000000−22−22−22−2200000000002i−2ii2−i2i2−i2i2−i2i2−i2000000000000
χ482-22-222-2-220022-2-2002-2-2-2-22200−22−22−22−2200-2-20022−2i2i−2i2i0000000000−22−22−22−220000000000−2i2i−i2i2−i2i2−i2i2−i2i2000000000000
χ492-22-222-2-2200-2-222002-2-2-2-22200−i2i2−i2i2i2−i2i2−i2002200-2-22i−2i2i−2i0000000000−i2i2−i2i2i2−i2i2−i20000000000−2i2i−22−222−22−2000000000000
χ502-22-222-2-2200-2-222002-2-2-2-22200−i2i2−i2i2i2−i2i2−i2002200-2-2−2i2i−2i2i0000000000−i2i2−i2i2i2−i2i2−i200000000002i−2i2−22−2−22−22000000000000
χ512-22-222-2-2200-2-222002-2-2-2-22200i2−i2i2−i2−i2i2−i2i2002200-2-22i−2i2i−2i0000000000i2−i2i2−i2−i2i2−i2i20000000000−2i2i2−22−2−22−22000000000000
χ522-22-222-2-2200-2-222002-2-2-2-22200i2−i2i2−i2−i2i2−i2i2002200-2-2−2i2i−2i2i0000000000i2−i2i2−i2−i2i2−i2i200000000002i−2i−22−222−22−2000000000000
χ532-2-22-222-222i−2i2i−2i−2i2i2i−2i-22-2-222-22-2000000002i−2i−2i2i2i−2i2i−2i0000000000002-200000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000
χ542-2-22-222-222i−2i2i−2i−2i2i2i−2i-22-2-222-22-2000000002i−2i−2i2i2i−2i2i−2i0000000000002-2000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000
χ552-2-22-222-222i−2i−2i2i2i−2i2i−2i-22-2-222-2-22−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232i−2i2i−2i2i−2i−2i2i000000000000-22−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000
χ562-2-22-222-222i−2i−2i2i2i−2i2i−2i-22-2-222-2-222ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232i−2i2i−2i2i−2i−2i2i000000000000-222ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000
χ572-2-22-222-22−2i2i2i−2i−2i2i−2i2i-22-2-222-2-222ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2i2i−2i2i−2i2i2i−2i000000000000-222ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ582-2-22-222-22−2i2i2i−2i−2i2i−2i2i-22-2-222-2-22−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2i2i−2i2i−2i2i2i−2i000000000000-22−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000
χ592-2-22-222-22−2i2i−2i2i2i−2i−2i2i-22-2-222-22-200000000−2i2i2i−2i−2i2i−2i2i0000000000002-2000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000
χ602-2-22-222-22−2i2i−2i2i2i−2i−2i2i-22-2-222-22-200000000−2i2i2i−2i−2i2i−2i2i0000000000002-200000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000
χ612-2-22-222-2-12i−2i−2i2i2i−2i2i−2i1-111-1-11-22−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−ii−ii−iii−i0000000000001-1ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300000000000000−i3i33−3000000
χ622-2-22-222-2-12i−2i−2i2i2i−2i2i−2i1-111-1-11-22−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−ii−ii−iii−i0000000000001-1ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000000000000i3−i3−33000000
χ632-2-22-222-2-12i−2i−2i2i2i−2i2i−2i1-111-1-11-222ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−ii−ii−iii−i0000000000001-1−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300000000000000i3−i3−33000000
χ642-2-22-222-2-12i−2i−2i2i2i−2i2i−2i1-111-1-11-222ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−ii−ii−iii−i0000000000001-1−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000000000000−i3i33−3000000
χ652-2-22-222-2-1−2i2i2i−2i−2i2i−2i2i1-111-1-11-222ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13i−ii−ii−i−ii0000000000001-1−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300000000000000i3−i33−3000000
χ662-2-22-222-2-1−2i2i2i−2i−2i2i−2i2i1-111-1-11-222ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13i−ii−ii−i−ii0000000000001-1−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ2300000000000000−i3i3−33000000
χ672-2-22-222-2-1−2i2i2i−2i−2i2i−2i2i1-111-1-11-22−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13i−ii−ii−i−ii0000000000001-1ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300000000000000−i3i3−33000000
χ682-2-22-222-2-1−2i2i2i−2i−2i2i−2i2i1-111-1-11-22−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13i−ii−ii−i−ii0000000000001-1ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ2300000000000000i3−i33−3000000
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χ9588-8-88-88-8-400000000444-4-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-8-888-400000000-44-44-444000000000000000000000000000000000000000000000000000000000000000000000000

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