Finite Group Databasebeta

← Group #10697107

Character table — Group #10697107

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order122222344444444666666644888888881212121212121212121212122424242424242424242424242424242444441212121212121212888888884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ922222222-2-222-2-222222222-2-200000000-2-2-2-22222-2-2-2-2000000000000000000000000000022-2-200000000
χ1022222222-2-222-2-222222222-2-200000000-2-2-2-22222-2-2-2-20000000000000000000000000000-2-22200000000
χ112222222-222-2-2-2-2-222222222-2000000002222-2-2-2-2-2-2-2-2000000000000000000000000000000000000002i−2i
χ122222222-222-2-2-2-2-222222222-2000000002222-2-2-2-2-2-2-2-200000000000000000000000000000000000000−2i2i
χ132222222-2-2-2-2-222-22222222-2200000000-2-2-2-2-2-2-2-222220000000000000000002-2000022-2-2000000000000
χ142222222-2-2-2-2-222-22222222-2200000000-2-2-2-2-2-2-2-22222000000000000000000-220000-2-222000000000000
χ15222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-11111000000000000
χ18222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-1000000000000
χ19222222-1-2-2-2-2-222-2-1-1-1-1-1-1-1-220000000011111111-1-1-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3002-2−i3−i3i3i3-1-111000000000000
χ20222222-1-2-2-2-2-222-2-1-1-1-1-1-1-1-220000000011111111-1-1-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i300-22i3i3−i3−i311-1-1000000000000
χ21222222-1-2-2-2-2-222-2-1-1-1-1-1-1-1-220000000011111111-1-1-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3002-2i3i3−i3−i3-1-111000000000000
χ22222222-1-2-2-2-2-222-2-1-1-1-1-1-1-1-220000000011111111-1-1-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i300-22−i3−i3i3i311-1-1000000000000
χ232222-2-22222-2-2-2-22-2-2-2-2222-222222-2-2-2-222-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ242222-2-22222-2-2-2-22-2-2-2-2222-22-2-2-2-2222222-2-222-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ252222-2-222-2-2-2-2222-2-2-2-22222-200000000-2-22222-2-222-2-20000000000000000000000000000000022-2-20000
χ262222-2-222-2-2-2-2222-2-2-2-22222-200000000-2-22222-2-222-2-200000000000000000000000000000000-2-2220000
χ272222-2-22-2222222-2-2-2-2-2222-2-20000000022-2-2-2-22222-2-20000000000000000000000000000000000002-200
χ282222-2-22-2222222-2-2-2-2-2222-2-20000000022-2-2-2-22222-2-2000000000000000000000000000000000000-2200
χ292222-2-22-2-2-222-2-2-2-2-2-2-22222200000000-2-222-2-222-2-22200000000000000002-2002-22-20000000000000000
χ302222-2-22-2-2-222-2-2-2-2-2-2-22222200000000-2-222-2-222-2-2220000000000000000-2200-22-220000000000000000
χ312222-2-2-1222-2-2-2-221111-1-1-1-222222-2-2-2-2-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111110000−i3i3i3−i3−i3i3−i3i3000000000000
χ322222-2-2-1222-2-2-2-221111-1-1-1-222222-2-2-2-2-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111110000i3−i3−i3i3i3−i3i3−i3000000000000
χ332222-2-2-1222-2-2-2-221111-1-1-1-22-2-2-2-22222-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-10000−i3i3i3−i3i3−i3i3−i3000000000000
χ342222-2-2-1222-2-2-2-221111-1-1-1-22-2-2-2-22222-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-10000i3−i3−i3i3−i3i3−i3i3000000000000
χ352222-2-2-1-2-2-222-2-2-21111-1-1-1220000000011-1-111-1-111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-200-11-11−i3i3i3−i3000000000000
χ362222-2-2-1-2-2-222-2-2-21111-1-1-1220000000011-1-111-1-111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-22001-11-1i3−i3−i3i3000000000000
χ372222-2-2-1-2-2-222-2-2-21111-1-1-1220000000011-1-111-1-111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-200-11-11i3−i3−i3i3000000000000
χ382222-2-2-1-2-2-222-2-2-21111-1-1-1220000000011-1-111-1-111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-22001-11-1−i3i3i3−i3000000000000
χ3922-2-22-22-2002-200222-2-2-22-200−i2−i2i2i2−i2−i2i2i200002-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000002i−2i2−22−20000
χ4022-2-22-22-2002-200222-2-2-22-200−i2−i2i2i2−i2−i2i2i200002-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000−2i2i−22−220000
χ4122-2-22-22-2002-200222-2-2-22-200i2i2−i2−i2i2i2−i2−i200002-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000002i−2i−22−220000
χ4222-2-22-22-2002-200222-2-2-22-200i2i2−i2−i2i2i2−i2−i200002-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000−2i2i2−22−20000
χ4322-2-2-222-200-22002-2-222-22-200−i2−i2i2i2i2i2−i2−i200002-2-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000002i−2i002−2−220000
χ4422-2-2-222-200-22002-2-222-22-200−i2−i2i2i2i2i2−i2−i200002-2-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000−2i2i00−222−20000
χ4522-2-2-222-200-22002-2-222-22-200i2i2−i2−i2−i2−i2i2i200002-2-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000002i−2i00−222−20000
χ4622-2-2-222-200-22002-2-222-22-200i2i2−i2−i2−i2−i2i2i200002-2-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000−2i2i002−2−220000
χ47444444-24-4-444-4-44-2-2-2-2-2-2-2-4-4000000002222-2-2-2-222220000000000000000000000000000000000000000
χ48444444-2-444-4-4-4-4-4-2-2-2-2-2-2-24-400000000-2-2-2-2222222220000000000000000000000000000000000000000
χ494444-4-4-24-4-4-4-44442222-2-2-24-40000000022-2-2-2-222-2-2220000000000000000000000000000000000000000
χ504444-4-4-2-4444444-42222-2-2-2-4-400000000-2-22222-2-2-2-2220000000000000000000000000000000000000000
χ5144-4-44-44400-4400-444-4-4-44-400000000000000-44-4400000000000000000000000000000000000000000000
χ5244-4-44-4-2400-4400-4-2-2222-22000000000000002-22-2000066−6−666−6−6−6−666−6−666000000000000000000000000
χ5344-4-44-4-2400-4400-4-2-2222-22000000000000002-22-20000−6−666−6−66666−6−666−6−6000000000000000000000000
χ5444-4-44-4-2-4004-4004-2-2222-2200−2i2−2i22i22i2−2i2−2i22i22i20000-22-220000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ5544-4-44-4-2-4004-4004-2-2222-22002i22i2−2i2−2i22i22i2−2i2−2i20000-22-220000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ5644-4-4-4444004-400-4-4-444-44-400000000000000-444-400000000000000000000000000000000000000000000
χ5744-4-4-44-24004-400-422-2-22-22000000000000002-2-22000066−6−6−6−666−6−66666−6−6000000000000000000000000
χ5844-4-4-44-24004-400-422-2-22-22000000000000002-2-220000−6−66666−6−666−6−6−6−666000000000000000000000000
χ5944-4-4-44-2-400-4400422-2-22-2200−2i2−2i22i22i22i22i2−2i2−2i20000-222-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ6044-4-4-44-2-400-4400422-2-22-22002i22i2−2i2−2i2−2i2−2i22i22i20000-222-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ614-44-400404-40000000004-4-400000022−2222−224-40000000000000022−2222−22000022−2222−22000000000000000000000000
χ624-44-400404-40000000004-4-4000000−2222−22224-400000000000000−2222−22220000−2222−2222000000000000000000000000
χ634-44-40040-440000000004-4-40022−2222−220000-44000000000022−2222−22000022−2222−220000000000000000000000000000
χ644-44-40040-440000000004-4-400−2222−22220000-440000000000−2222−22220000−2222−22220000000000000000000000000000
χ654-44-400-204-400000−2i32i3−2i32i3-22200000022−2222−22-22−2i32i300000000i6−i6i6−i6−22−22−i6i6−i6i6−22−22000000000000000000000000
χ664-44-400-204-400000−2i32i3−2i32i3-222000000−2222−2222-22−2i32i300000000−i6i6−i6i62−22−2i6−i6i6−i62−22−2000000000000000000000000
χ674-44-400-204-4000002i3−2i32i3−2i3-22200000022−2222−22-222i3−2i300000000−i6i6−i6i6−22−22i6−i6i6−i6−22−22000000000000000000000000
χ684-44-400-204-4000002i3−2i32i3−2i3-222000000−2222−2222-222i3−2i300000000i6−i6i6−i62−22−2−i6i6−i6i62−22−2000000000000000000000000
χ694-44-400-20-4400000−2i32i3−2i32i3-2220022−2222−2200002-22i3−2i300000000−22−22i6−i6i6−i6−22−22−i6i6−i6i6000000000000000000000000
χ704-44-400-20-4400000−2i32i3−2i32i3-22200−2222−222200002-22i3−2i3000000002−22−2−i6i6−i6i62−22−2i6−i6i6−i6000000000000000000000000
χ714-44-400-20-44000002i3−2i32i3−2i3-2220022−2222−2200002-2−2i32i300000000−22−22−i6i6−i6i6−22−22i6−i6i6−i6000000000000000000000000
χ724-44-400-20-44000002i3−2i32i3−2i3-22200−2222−222200002-2−2i32i3000000002−22−2i6−i6i6−i62−22−2−i6i6−i6i6000000000000000000000000
χ734-4-44004000004-400000-4-44002i−2i−2i2i2i−2i−2i2i000000004-4002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ744-4-44004000004-400000-4-4400−2i2i2i−2i−2i2i2i−2i000000004-400−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ754-4-4400400000-4400000-4-44002i−2i−2i2i−2i2i2i−2i00000000-44002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ764-4-4400400000-4400000-4-4400−2i2i2i−2i2i−2i−2i2i00000000-4400−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ774-4-4400-2000004-40−2i32i32i3−2i322-2002i−2i−2i2i2i−2i−2i2i00000000-22−2i32i32ζ14−2ζ14−2ζ142ζ142ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ222ζ22−2ζ22−2ζ222ζ22000000000000000000000000
χ784-4-4400-2000004-40−2i32i32i3−2i322-200−2i2i2i−2i−2i2i2i−2i00000000-22−2i32i3−2ζ142ζ142ζ14−2ζ14−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22−2ζ222ζ222ζ22−2ζ22000000000000000000000000
χ794-4-4400-2000004-402i3−2i3−2i32i322-2002i−2i−2i2i2i−2i−2i2i00000000-222i3−2i32ζ22−2ζ22−2ζ222ζ222ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ142ζ14−2ζ14−2ζ142ζ14000000000000000000000000
χ804-4-4400-2000004-402i3−2i3−2i32i322-200−2i2i2i−2i−2i2i2i−2i00000000-222i3−2i3−2ζ222ζ222ζ22−2ζ22−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14−2ζ142ζ142ζ14−2ζ14000000000000000000000000
χ814-4-4400-200000-440−2i32i32i3−2i322-2002i−2i−2i2i−2i2i2i−2i000000002-22i3−2i32ζ22−2ζ22−2ζ222ζ22−2ζ222ζ222ζ22−2ζ222ζ14−2ζ14−2ζ142ζ14−2ζ142ζ142ζ14−2ζ14000000000000000000000000
χ824-4-4400-200000-440−2i32i32i3−2i322-200−2i2i2i−2i2i−2i−2i2i000000002-22i3−2i3−2ζ222ζ222ζ22−2ζ222ζ22−2ζ22−2ζ222ζ22−2ζ142ζ142ζ14−2ζ142ζ14−2ζ14−2ζ142ζ14000000000000000000000000
χ834-4-4400-200000-4402i3−2i3−2i32i322-2002i−2i−2i2i−2i2i2i−2i000000002-2−2i32i32ζ14−2ζ14−2ζ142ζ14−2ζ142ζ142ζ14−2ζ142ζ22−2ζ22−2ζ222ζ22−2ζ222ζ222ζ22−2ζ22000000000000000000000000
χ844-4-4400-200000-4402i3−2i3−2i32i322-200−2i2i2i−2i2i−2i−2i2i000000002-2−2i32i3−2ζ142ζ142ζ14−2ζ142ζ14−2ζ14−2ζ142ζ14−2ζ222ζ222ζ22−2ζ222ζ22−2ζ22−2ζ222ζ22000000000000000000000000

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