Finite Group Databasebeta

← Group #10698948

Character table — Group #10698948

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212128888121224242424242424244444121212121212121222448888888888
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
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ9222222222-2-222222-2-2-2222222-2-2-2-20000-2-20000000000000000000022-2-20000000000
χ10222222222-2-222222-2-2-2222222-2-2-2-20000-2-200000000000000000000-2-2220000000000
χ112222222-2-222-2-22222-2-222-2-2-2-222-2-200002-200000000000000000000000000002i2i−2i−2i00
χ122222222-2-222-2-22222-2-222-2-2-2-222-2-200002-20000000000000000000000000000−2i−2i2i2i00
χ132222222-2-2-2-2-2-2222-22222-2-2-2-2-2-22222-2-2-222222-2-2-2-200000000000000000000000000
χ142222222-2-2-2-2-2-2222-22222-2-2-2-2-2-222-2-222-22-2-2-2-2222200000000000000000000000000
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
χ19222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111-1-122-2-21-1-1-1-1-111110000−i3−i3i3i3−i3−i3i3i300000000000000
χ20222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111-1-122-2-21-1-1-1-1-111110000i3i3−i3−i3i3i3−i3−i300000000000000
χ21222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111-1-1-2-2221-11111-1-1-1-10000−i3−i3i3i3i3i3−i3−i300000000000000
χ22222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111-1-1-2-2221-11111-1-1-1-10000i3i3−i3−i3−i3−i3i3i300000000000000
χ232222-2-222222-2-2222-2-22-2-222-2-222-2-20000-2200000000002i−2i00002i−2i2i−2i00000000000000
χ242222-2-222222-2-2222-2-22-2-222-2-222-2-20000-220000000000−2i2i0000−2i2i−2i2i00000000000000
χ252222-2-2222-2-2-2-222222-2-2-222-2-2-2-22200002-20000000000000000000000002i2i−2i−2i000000
χ262222-2-2222-2-2-2-222222-2-2-222-2-2-2-22200002-2000000000000000000000000−2i−2i2i2i000000
χ272222-2-22-2-22222222-22-2-2-2-2-22222220000-2-2000000000000000000000000000000002-2
χ282222-2-22-2-22222222-22-2-2-2-2-22222220000-2-200000000000000000000000000000000-22
χ292222-2-22-2-2-2-2222222-22-2-2-2-222-2-2-2-2000022000000002-2002-22-2000000000000000000
χ302222-2-22-2-2-2-2222222-22-2-2-2-222-2-2-2-200002200000000-2200-22-22000000000000000000
χ312222-2-2-12222-2-2-1-1-1-2-2211-1-111-1-11100001-133−3−333−3−3002i−2i−i3i3i3−i3−ii−ii00000000000000
χ322222-2-2-12222-2-2-1-1-1-2-2211-1-111-1-11100001-133−3−333−3−300−2i2ii3−i3−i3i3i−ii−i00000000000000
χ332222-2-2-12222-2-2-1-1-1-2-2211-1-111-1-11100001-1−3−333−3−333002i−2ii3−i3−i3i3−ii−ii00000000000000
χ342222-2-2-12222-2-2-1-1-1-2-2211-1-111-1-11100001-1−3−333−3−33300−2i2i−i3i3i3−i3i−ii−i00000000000000
χ352222-2-2-1-2-2-2-222-1-1-12-221111-1-111110000-1-133−3−3−3−3332-200-11-113−3−3300000000000000
χ362222-2-2-1-2-2-2-222-1-1-12-221111-1-111110000-1-133−3−3−3−333-22001-11-1−333−300000000000000
χ372222-2-2-1-2-2-2-222-1-1-12-221111-1-111110000-1-1−3−33333−3−32-200-11-11−333−300000000000000
χ382222-2-2-1-2-2-2-222-1-1-12-221111-1-111110000-1-1−3−33333−3−3-22001-11-13−3−3300000000000000
χ3922-2-2-2222-2002-22-2-2000-222-22-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2000000000000002i−2i00002−22−200
χ4022-2-2-2222-2002-22-2-2000-222-22-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i200000000000000−2i2i0000−22−2200
χ4122-2-2-2222-2002-22-2-2000-222-22-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2000000000000002i−2i0000−22−2200
χ4222-2-2-2222-2002-22-2-2000-222-22-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i200000000000000−2i2i00002−22−200
χ4322-2-2-222-2200-222-2-2000-22-22-220000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i20000000000002-2000000−i2i2i2−i200
χ4422-2-2-222-2200-222-2-2000-22-22-220000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i2000000000000-22000000i2−i2−i2i200
χ4522-2-2-222-2200-222-2-2000-22-22-220000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i20000000000002-2000000i2−i2−i2i200
χ4622-2-2-222-2200-222-2-2000-22-22-220000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i2000000000000-22000000−i2i2i2−i200
χ47444444-244-4-444-2-2-2-4-4-4-2-2-2-2-2-222220000220000000000000000000000000000000000
χ48444444-2-4-444-4-4-2-2-24-4-4-2-22222-2-2220000-220000000000000000000000000000000000
χ494444-4-4-244-4-4-4-4-2-2-244-422-2-22222-2-20000-220000000000000000000000000000000000
χ504444-4-4-2-4-44444-2-2-2-44-42222-2-2-2-2-2-20000220000000000000000000000000000000000
χ5144-4-44-444-400-444-4-40004-44-4-4400000000000000000000000000000000000000000000
χ5244-4-44-44-44004-44-4-40004-4-444-400000000000000000000000000000000000000000000
χ5344-4-44-4-24-400-44-222000-22-222-20000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ5444-4-44-4-24-400-44-222000-22-222-20000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ5544-4-44-4-2-44004-4-222000-222-2-220000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ5644-4-44-4-2-44004-4-222000-222-2-220000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ5744-4-4-44-24-4004-4-2220002-2-22-220000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ5844-4-4-44-24-4004-4-2220002-2-22-2200002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ5944-4-4-44-2-4400-44-2220002-22-22-20000−2i22i22i2−2i200i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ6044-4-4-44-2-4400-44-2220002-22-22-200002i2−2i2−2i22i200−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ614-44-4004004i−4i00-44-40000000004i−4i000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ624-44-4004004i−4i00-44-40000000004i−4i00000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ634-44-400400−4i4i00-44-4000000000−4i4i00000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ644-44-400400−4i4i00-44-4000000000−4i4i000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ658-88-800-4008i−8i004-44000000000−4i4i000000000000000000000000000000000000000000
χ668-88-800-400−8i8i004-440000000004i−4i000000000000000000000000000000000000000000
χ678-8-88008000000-8-8800000000000000000000000000000000000000000000000000000
χ688-8-8800-400000044-40000000000043−430000000000000000000000000000000000000000
χ698-8-8800-400000044-400000000000−43430000000000000000000000000000000000000000

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