Finite Group Databasebeta

← Group #10697249

Character table — Group #10697249

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
χ9222222222-2-222222-2-2-222222-2-2-2-220000-2-20000000000000000000022-2-20000000000
χ10222222222-2-222222-2-2-222222-2-2-2-220000-2-200000000000000000000-2-2220000000000
χ112222222-2-222-2-22222-2-222-2-2-222-2-2-22i2i−2i−2i-222i2i2i2i−2i−2i−2i−2i00000000000000000000000000
χ122222222-2-222-2-22222-2-222-2-2-222-2-2-2−2i−2i2i2i-22−2i−2i−2i−2i2i2i2i2i00000000000000000000000000
χ132222222-2-2-2-2-2-2222-22222-2-2-2-2-222-200002-2000000000000000000000000000022-2-200
χ142222222-2-2-2-2-2-2222-22222-2-2-2-2-222-200002-20000000000000000000000000000-2-22200
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
χ19222222-1-2-222-2-2-1-1-12-2-2-1-1111-1-11112i2i−2i−2i1-1−i−i−i−iiiii0000−i3−i3i3i333−3−300000000000000
χ20222222-1-2-222-2-2-1-1-12-2-2-1-1111-1-11112i2i−2i−2i1-1−i−i−i−iiiii0000i3i3−i3−i3−3−33300000000000000
χ21222222-1-2-222-2-2-1-1-12-2-2-1-1111-1-1111−2i−2i2i2i1-1iiii−i−i−i−i0000−i3−i3i3i3−3−33300000000000000
χ22222222-1-2-222-2-2-1-1-12-2-2-1-1111-1-1111−2i−2i2i2i1-1iiii−i−i−i−i0000i3i3−i3−i333−3−300000000000000
χ232222-2-222-2222-2222-2-22-2-22-2-222-2-2200002-2000000000000000000000000000000002-2
χ242222-2-222-2222-2222-2-22-2-22-2-222-2-2200002-200000000000000000000000000000000-22
χ252222-2-222-2-2-22-222222-2-2-22-2-2-2-22220000-2200000000002-200002-22-200000000000000
χ262222-2-222-2-2-22-222222-2-2-22-2-2-2-22220000-220000000000-220000-22-2200000000000000
χ272222-2-22-2222-22222-22-2-2-2-2222222-20000-2-200000000000000000000000022-2-2000000
χ282222-2-22-2222-22222-22-2-2-2-2222222-20000-2-2000000000000000000000000-2-222000000
χ292222-2-22-22-2-2-222222-22-2-2-222-2-2-2-2-2000022000000002-2002-22-2000000000000000000
χ302222-2-22-22-2-2-222222-22-2-2-222-2-2-2-2-200002200000000-2200-22-22000000000000000000
χ312222-2-2-12-2-2-22-2-1-1-122-211-11111-1-1-100001-1−i3−i3i3i3−i3−i3i3i3002-2−i3i3i3−i3-11-1100000000000000
χ322222-2-2-12-2-2-22-2-1-1-122-211-11111-1-1-100001-1−i3−i3i3i3−i3−i3i3i300-22i3−i3−i3i31-11-100000000000000
χ332222-2-2-12-2-2-22-2-1-1-122-211-11111-1-1-100001-1i3i3−i3−i3i3i3−i3−i3002-2i3−i3−i3i3-11-1100000000000000
χ342222-2-2-12-2-2-22-2-1-1-122-211-11111-1-1-100001-1i3i3−i3−i3i3i3−i3−i300-22−i3i3i3−i31-11-100000000000000
χ352222-2-2-1-22-2-2-22-1-1-12-22111-1-1111110000-1-133−3−3−3−3332-200-11-113−3−3300000000000000
χ362222-2-2-1-22-2-2-22-1-1-12-22111-1-1111110000-1-133−3−3−3−333-22001-11-1−333−300000000000000
χ372222-2-2-1-22-2-2-22-1-1-12-22111-1-1111110000-1-1−3−33333−3−32-200-11-11−333−300000000000000
χ382222-2-2-1-22-2-2-22-1-1-12-22111-1-1111110000-1-1−3−33333−3−3-22001-11-13−3−3300000000000000
χ3922-2-22-222200-2-22-2-20002-222-20000-22−22−2002−22−22−22−20000000000002-20000002−22−200
χ4022-2-22-222200-2-22-2-20002-222-20000-22−22−2002−22−22−22−2000000000000-22000000−22−2200
χ4122-2-22-222200-2-22-2-20002-222-20000-2−22−2200−22−22−22−220000000000002-2000000−22−2200
χ4222-2-22-222200-2-22-2-20002-222-20000-2−22−2200−22−22−22−22000000000000-220000002−22−200
χ4322-2-22-22-2-200222-2-20002-2-2-2200002−i2i2i2−i200−i2i2−i2i2i2−i2i2−i2000000000000002i−2i00002−2−2200
χ4422-2-22-22-2-200222-2-20002-2-2-2200002−i2i2i2−i200−i2i2−i2i2i2−i2i2−i200000000000000−2i2i0000−222−200
χ4522-2-22-22-2-200222-2-20002-2-2-2200002i2−i2−i2i200i2−i2i2−i2−i2i2−i2i2000000000000002i−2i0000−222−200
χ4622-2-22-22-2-200222-2-20002-2-2-2200002i2−i2−i2i200i2−i2i2−i2−i2i2−i2i200000000000000−2i2i00002−2−2200
χ47444444-244-4-444-2-2-2-4-4-4-2-2-2-2-22222-20000220000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-2-2-2-444-2-222222-2-220000-220000000000000000000000000000000000
χ494444-4-4-24-4444-4-2-2-2-4-4422-222-2-222-20000-220000000000000000000000000000000000
χ504444-4-4-2-4444-44-2-2-2-44-4222-2-2-2-2-2-220000220000000000000000000000000000000000
χ5144-4-44-4-24400-4-4-222000-22-2-220000222−2222−2200−22−22−22−2200000000000000000000000000
χ5244-4-44-4-24400-4-4-222000-22-2-2200002−2222−2222002−22−22−22−200000000000000000000000000
χ5344-4-44-4-2-4-40044-222000-2222-20000-2−2i22i22i2−2i200i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ5444-4-44-4-2-4-40044-222000-2222-20000-22i2−2i2−2i22i200−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ5544-4-4-4444-400-444-4-4000-444-440000-40000000000000000000000000000000000000000
χ5644-4-4-444-44004-44-4-4000-44-44-4000040000000000000000000000000000000000000000
χ5744-4-4-44-24-400-44-2220002-2-22-200002000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ5844-4-4-44-24-400-44-2220002-2-22-200002000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ5944-4-4-44-2-44004-4-2220002-22-220000-20000006−6−66−666−600000000000000000000000000
χ6044-4-4-44-2-44004-4-2220002-22-220000-2000000−666−66−6−6600000000000000000000000000
χ614-44-4004004-400-4-44000000004-400000000000000000000000000000000000−2i22i2000000
χ624-44-4004004-400-4-44000000004-4000000000000000000000000000000000002i2−2i2000000
χ634-44-400400-4400-4-4400000000-44000000000000000000000000000000000−2i22i200000000
χ644-44-400400-4400-4-4400000000-440000000000000000000000000000000002i2−2i200000000
χ658-88-800-4008-80044-400000000-440000000000000000000000000000000000000000000
χ668-88-800-400-880044-4000000004-40000000000000000000000000000000000000000000
χ678-8-88008000000-88-800000000000000000000000000000000000000000000000000000
χ688-8-8800-40000004-440000000000−4i34i300000000000000000000000000000000000000000
χ698-8-8800-40000004-4400000000004i3−4i300000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).