Finite Group Databasebeta

← Group #10698973

Character table — Group #10698973

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212128888121224242424242424244488121212122424242444448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ92222222222-2-22222-2-2-222222-2-2-2-220000-2-20000000000000000000022-2-20000000000
χ102222222222-2-22222-2-2-222222-2-2-2-220000-2-200000000000000000000-2-2220000000000
χ112222222-2-2-222-22222-2-222-2-2-222-2-2-22i2i−2i−2i2-22i2i2i2i−2i−2i−2i−2i00000000000000000000000000
χ122222222-2-2-222-22222-2-222-2-2-222-2-2-2−2i−2i2i2i2-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000000
χ132222222-2-2-2-2-2-2222-22222-2-2-2-2-222-20000-22000000000000000000000000000022-2-200
χ142222222-2-2-2-2-2-2222-22222-2-2-2-2-222-20000-220000000000000000000000000000-2-22200
χ15222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ16222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ17222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1111100000000000000
χ18222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-100000000000000
χ19222222-1-2-2-222-2-1-1-12-2-2-1-1111-1-11112i2i−2i−2i-11−i−i−i−iiiii0000−i3−i3i3i333−3−300000000000000
χ20222222-1-2-2-222-2-1-1-12-2-2-1-1111-1-11112i2i−2i−2i-11−i−i−i−iiiii0000i3i3−i3−i3−3−33300000000000000
χ21222222-1-2-2-222-2-1-1-12-2-2-1-1111-1-1111−2i−2i2i2i-11iiii−i−i−i−i0000−i3−i3i3i3−3−33300000000000000
χ22222222-1-2-2-222-2-1-1-12-2-2-1-1111-1-1111−2i−2i2i2i-11iiii−i−i−i−i0000i3i3−i3−i333−3−300000000000000
χ232222-2-2222-222-2222-22-2-2-222-22222-20000-2-2000000002i−2i002i−2i2i−2i000000000000000000
χ242222-2-2222-222-2222-22-2-2-222-22222-20000-2-200000000−2i2i00−2i2i−2i2i000000000000000000
χ252222-2-2222-2-2-2-22222-22-2-222-2-2-2-2-2-20000220000000000000000000000002i2i−2i−2i000000
χ262222-2-2222-2-2-2-22222-22-2-222-2-2-2-2-2-2000022000000000000000000000000−2i−2i2i2i000000
χ272222-2-22-2-22222222-2-22-2-2-2-2222-2-220000-2200000000002-200002-22-200000000000000
χ282222-2-22-2-22222222-2-22-2-2-2-2222-2-220000-220000000000-220000-22-2200000000000000
χ292222-2-22-2-22-2-2222222-2-2-2-2-22-2-222200002-2000000000000000000000000000000002-2
χ302222-2-22-2-22-2-2222222-2-2-2-2-22-2-222200002-200000000000000000000000000000000-22
χ312222-2-2-122-222-2-1-1-1-22-211-1-11-1-1-1-11000011−i3−i3i3i3−i3−i3i3i32i−2i00−ii−ii3−3−3300000000000000
χ322222-2-2-122-222-2-1-1-1-22-211-1-11-1-1-1-11000011−i3−i3i3i3−i3−i3i3i3−2i2i00i−ii−i−333−300000000000000
χ332222-2-2-122-222-2-1-1-1-22-211-1-11-1-1-1-11000011i3i3−i3−i3i3i3−i3−i32i−2i00−ii−ii−333−300000000000000
χ342222-2-2-122-222-2-1-1-1-22-211-1-11-1-1-1-11000011i3i3−i3−i3i3i3−i3−i3−2i2i00i−ii−i3−3−3300000000000000
χ352222-2-2-1-2-22222-1-1-1-2-221111-1-1-111-100001-133−3−3−3−333002-2−333−3-11-1100000000000000
χ362222-2-2-1-2-22222-1-1-1-2-221111-1-1-111-100001-133−3−3−3−33300-223−3−331-11-100000000000000
χ372222-2-2-1-2-22222-1-1-1-2-221111-1-1-111-100001-1−3−33333−3−3002-23−3−33-11-1100000000000000
χ382222-2-2-1-2-22222-1-1-1-2-221111-1-1-111-100001-1−3−33333−3−300-22−333−31-11-100000000000000
χ3922-2-22-222-2200-22-2-20002-22-220000-22−22−2002−22−22−22−20000000000002-20000002−22−200
χ4022-2-22-222-2200-22-2-20002-22-220000-22−22−2002−22−22−22−2000000000000-22000000−22−2200
χ4122-2-22-222-2200-22-2-20002-22-220000-2−22−2200−22−22−22−220000000000002-2000000−22−2200
χ4222-2-22-222-2200-22-2-20002-22-220000-2−22−2200−22−22−22−22000000000000-220000002−22−200
χ4322-2-22-22-22-20022-2-20002-2-22-200002−i2i2i2−i200−i2i2−i2i2i2−i2i2−i2000000000000002i−2i00002−2−2200
χ4422-2-22-22-22-20022-2-20002-2-22-200002−i2i2i2−i200−i2i2−i2i2i2−i2i2−i200000000000000−2i2i0000−222−200
χ4522-2-22-22-22-20022-2-20002-2-22-200002i2−i2−i2i200i2−i2i2−i2−i2i2−i2i2000000000000002i−2i0000−222−200
χ4622-2-22-22-22-20022-2-20002-2-22-200002i2−i2−i2i200i2−i2i2−i2−i2i2−i2i200000000000000−2i2i00002−2−2200
χ47444444-2444-4-44-2-2-2-4-4-4-2-2-2-2-22222-20000220000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-2-2-2-444-2-222222-2-2200002-20000000000000000000000000000000000
χ494444-4-4-244-4-4-4-4-2-2-24-4422-2-22222220000-2-20000000000000000000000000000000000
χ504444-4-4-2-4-44-4-44-2-2-244-42222-222-2-2-20000-220000000000000000000000000000000000
χ5144-4-44-4-24-4400-4-222000-22-22-20000222−2222−2200−22−22−22−2200000000000000000000000000
χ5244-4-44-4-24-4400-4-222000-22-22-200002−2222−2222002−22−22−22−200000000000000000000000000
χ5344-4-44-4-2-44-4004-222000-222-220000-2−2i22i22i2−2i200i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ5444-4-44-4-2-44-4004-222000-222-220000-22i2−2i2−2i22i200−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ5544-4-4-4444-4-40044-4-4000-444-4-4000040000000000000000000000000000000000000000
χ5644-4-4-444-44400-44-4-4000-44-4440000-40000000000000000000000000000000000000000
χ5744-4-4-44-24-4-4004-2220002-2-2220000-2000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ5844-4-4-44-24-4-4004-2220002-2-2220000-2000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ5944-4-4-44-2-44400-4-2220002-22-2-2000020000006−6−66−666−600000000000000000000000000
χ6044-4-4-44-2-44400-4-2220002-22-2-200002000000−666−66−6−6600000000000000000000000000
χ614-4-440040004i−4i0-44-4000000004i−4i0000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ624-4-440040004i−4i0-44-4000000004i−4i000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ634-4-44004000−4i4i0-44-400000000−4i4i000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ644-4-44004000−4i4i0-44-400000000−4i4i0000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ658-88-8008000000-8-8800000000000000000000000000000000000000000000000000000
χ668-88-800-400000044-4000000000043−4300000000000000000000000000000000000000000
χ678-88-800-400000044-40000000000−434300000000000000000000000000000000000000000
χ688-8-8800-40008i−8i04-4400000000−4i4i0000000000000000000000000000000000000000000
χ698-8-8800-4000−8i8i04-44000000004i−4i0000000000000000000000000000000000000000000

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