Finite Group Databasebeta

← Group #10773129

Character table — Group #10773129

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222224444444444444444444444444444444444444444888816161616161616161616242424242424242448484848
order122234444446661212121224446688888888121212121212121212122424242424242424242424242424242444442466121212121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1
χ91111111-1-111111-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11-11111-1-1-1-11-11-11-11-11-11-1
χ101111111-1-111111-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11-11111-1-1-1-1-11-11-11-11-11-11
χ111111111-1-111111-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-11-1-1-1-111111-1-111-1-111-1-11
χ121111111-1-111111-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-11-1-1-1-11111-111-1-111-1-111-1
χ131111111-1-111111-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-11-1-111-1-1111-11-11-11-1-11-11
χ141111111-1-111111-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-11-1-111-1-111-11-11-11-111-11-1
χ151111111-1-111111-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111-111-1-111-1-11-1-111-1-11-111-1
χ161111111-1-111111-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111-111-1-111-1-1-111-1-111-11-1-11
χ17222222-2222-22222222-22-2-2-2-20000000022-2-222-2-2-2-2000000000000000000000000000000002200-2-20000
χ18222222-2222-22222222-22-2-2-2-20000000022-2-222-2-2-2-200000000000000000000000000000000-2-200220000
χ19222222-2-2-22-2222-2-2-2-22-22-2220000000022-2-2-2-222-2-2000000000000000000000000000000002-200-220000
χ20222222-2-2-22-2222-2-2-2-22-22-2220000000022-2-2-2-222-2-200000000000000000000000000000000-22002-20000
χ2122222-2222-222222222-2-22-2-2-200000000-2-222-2-222-2-20000000000000000000000000000002200-2-2000000
χ2222222-2222-222222222-2-22-2-2-200000000-2-222-2-222-2-2000000000000000000000000000000-2-20022000000
χ2322222-22-2-2-22222-2-2-2-222-2-22200000000-2-22222-2-2-2-20000000000000000000000000000002-200-22000000
χ2422222-22-2-2-22222-2-2-2-222-2-22200000000-2-22222-2-2-2-2000000000000000000000000000000-22002-2000000
χ2522222-2-222-2-222222222-2-222200000000-2-2-2-2-2-2-2-22200000000000000002-22-200002-22-200000000000000
χ2622222-2-222-2-222222222-2-222200000000-2-2-2-2-2-2-2-2220000000000000000-22-220000-22-2200000000000000
χ2722222-2-2-2-2-2-2222-2-2-2-2-2222-2-200000000-2-2-2-222222200000000000000002-2-2200002-2-2200000000000000
χ2822222-2-2-2-2-2-2222-2-2-2-2-2222-2-200000000-2-2-2-22222220000000000000000-222-20000-222-200000000000000
χ292222-1222222-1-1-1-1-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1000000000000
χ302222-1222222-1-1-1-1-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111000000000000
χ312222-1222222-1-1-1-1-1-1-12222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111112222-2-211-1-1-1-111000000000000
χ322222-1222222-1-1-1-1-1-1-12222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-222-1-11111-1-1000000000000
χ332222-122-2-222-1-1-11111-2-2-22112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111122-2-22-2-1-1-1-11111000000000000
χ342222-122-2-222-1-1-11111-2-2-22112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-222-221111-1-1-1-1000000000000
χ352222-122-2-222-1-1-11111-2-2-2211-2-2-2-22222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-122-2-2-2211-1-111-1-1000000000000
χ362222-122-2-222-1-1-11111-2-2-2211-2-2-2-22222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-2-2222-2-1-111-1-111000000000000
χ372222-1-2-222-2-2-1-1-1-1-1-1-12-2-22-1-10000000011111111-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i32-22-200−i3i3-11-11−i3i3000000000000
χ382222-1-2-222-2-2-1-1-1-1-1-1-12-2-22-1-10000000011111111-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-22-2200i3−i31-11-1i3−i3000000000000
χ392222-1-2-222-2-2-1-1-1-1-1-1-12-2-22-1-10000000011111111-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i32-22-200i3−i3-11-11i3−i3000000000000
χ402222-1-2-222-2-2-1-1-1-1-1-1-12-2-22-1-10000000011111111-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-22-2200−i3i31-11-1−i3i3000000000000
χ412222-1-2-2-2-2-2-2-1-1-11111-222211000000001111-1-1-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-2-2200−i3i3-111-1i3−i3000000000000
χ422222-1-2-2-2-2-2-2-1-1-11111-222211000000001111-1-1-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-222-200i3−i31-1-11−i3i3000000000000
χ432222-1-2-2-2-2-2-2-1-1-11111-222211000000001111-1-1-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-2-2200i3−i3-111-1−i3i3000000000000
χ442222-1-2-2-2-2-2-2-1-1-11111-222211000000001111-1-1-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-222-200−i3i31-1-11i3−i3000000000000
χ454444-24-4444-4-2-2-2-2-2-2-2-44-4-42200000000-2-222-2-22222000000000000000000000000000000000000000000
χ464444-24-4-4-44-4-2-2-222224-44-4-2-200000000-2-22222-2-222000000000000000000000000000000000000000000
χ474444-2-4444-44-2-2-2-2-2-2-2-4-44-4220000000022-2-222-2-222000000000000000000000000000000000000000000
χ484444-2-44-4-4-44-2-2-2222244-4-4-2-20000000022-2-2-2-22222000000000000000000000000000000000000000000
χ4944-4-4404000-44-4-4000000000000002222−22−22004-4000000000000002222−22−222222−22−2200000000000000000000000000
χ5044-4-4404000-44-4-400000000000000−22−222222004-400000000000000−22−222222−22−22222200000000000000000000000000
χ5144-4-440-400044-4-40000000000−2i2−2i22i22i2000000-44000000−2i2−2i22i22i2−2i2−2i22i22i20000000000000000000000000000000000
χ5244-4-440-400044-4-400000000002i22i2−2i2−2i2000000-440000002i22i2−2i2−2i22i22i2−2i2−2i20000000000000000000000000000000000
χ5344-4-4-204000-4-2222323−23−2300000000002222−22−2200-220023−230066−6−6−6−666−2−222−2−22200000000000000000000000000
χ5444-4-4-204000-4-2222323−23−230000000000−22−22222200-220023−2300−6−66666−6−622−2−222−2−200000000000000000000000000
χ5544-4-4-204000-4-222−23−23232300000000002222−22−2200-2200−232300−6−66666−6−6−2−222−2−22200000000000000000000000000
χ5644-4-4-204000-4-222−23−2323230000000000−22−22222200-2200−23230066−6−6−6−66622−2−222−2−200000000000000000000000000
χ5744-4-4-20-40004-2222323−23−23000000−2i2−2i22i22i20000002-200−232300i2i2−i2−i2i2i2−i2−i2i6i6−i6−i6−i6−i6i6i600000000000000000000000000
χ5844-4-4-20-40004-2222323−23−230000002i22i2−2i2−2i20000002-200−232300−i2−i2i2i2−i2−i2i2i2−i6−i6i6i6i6i6−i6−i600000000000000000000000000
χ5944-4-4-20-40004-222−23−232323000000−2i2−2i22i22i20000002-20023−2300i2i2−i2−i2i2i2−i2−i2−i6−i6i6i6i6i6−i6−i600000000000000000000000000
χ6044-4-4-20-40004-222−23−2323230000002i22i2−2i2−2i20000002-20023−2300−i2−i2i2i2−i2−i2i2i2i6i6−i6−i6−i6−i6i6i600000000000000000000000000
χ614-44-444000-40-44-4000000000022−2222−2200004-40000000022−2222−2222−2222−220000000000000000000000000000000000
χ624-44-444000-40-44-40000000000−2222−222200004-400000000−2222−2222−2222−22220000000000000000000000000000000000
χ634-44-44-400040-44-400000000000000−2i22i2−2i22i2-440000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000
χ644-44-44-400040-44-4000000000000002i2−2i22i2−2i2-4400000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000
χ654-44-4-24000-402-2223−2323−2300000022−2222−220000-220023−230000−22−22−22−226−66−6−66−6600000000000000000000000000
χ664-44-4-24000-402-2223−2323−23000000−2222−22220000-220023−2300002−22−22−22−2−66−666−66−600000000000000000000000000
χ674-44-4-24000-402-22−2323−232300000022−2222−220000-2200−23230000−22−22−22−22−66−666−66−600000000000000000000000000
χ684-44-4-24000-402-22−2323−2323000000−2222−22220000-2200−232300002−22−22−22−26−66−6−66−6600000000000000000000000000
χ694-44-4-2-4000402-2223−2323−230000000000−2i22i2−2i22i22-200−23230000i6−i6i6−i6−i6i6−i6i6i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ704-44-4-2-4000402-2223−2323−2300000000002i2−2i22i2−2i22-200−23230000−i6i6−i6i6i6−i6i6−i6−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ714-44-4-2-4000402-22−2323−23230000000000−2i22i2−2i22i22-20023−230000−i6i6−i6i6i6−i6i6−i6i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ724-44-4-2-4000402-22−2323−232300000000002i2−2i22i2−2i22-20023−230000i6−i6i6−i6−i6i6−i6i6−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ734-4-444004-400-4-444-4-440000002i−2i−2i2i−2i2i2i−2i00000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ744-4-444004-400-4-444-4-44000000−2i2i2i−2i2i−2i−2i2i0000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ754-4-44400-4400-4-44-444-40000002i−2i−2i2i2i−2i−2i2i00000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ764-4-44400-4400-4-44-444-4000000−2i2i2i−2i−2i2i2i−2i0000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ774-4-44-2004-40022-2-222-20000−2i32i32i−2i−2i2i−2i2i2i−2i00000000−2i32i32ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ22−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ2200000000000000000000000000
χ784-4-44-2004-40022-2-222-20000−2i32i3−2i2i2i−2i2i−2i−2i2i00000000−2i32i3−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ222ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ2200000000000000000000000000
χ794-4-44-2004-40022-2-222-200002i3−2i32i−2i−2i2i−2i2i2i−2i000000002i3−2i32ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ14−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ1400000000000000000000000000
χ804-4-44-2004-40022-2-222-200002i3−2i3−2i2i2i−2i2i−2i−2i2i000000002i3−2i3−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ142ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ1400000000000000000000000000
χ814-4-44-200-440022-22-2-220000−2i32i32i−2i−2i2i2i−2i−2i2i000000002i3−2i32ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ1400000000000000000000000000
χ824-4-44-200-440022-22-2-220000−2i32i3−2i2i2i−2i−2i2i2i−2i000000002i3−2i3−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ1400000000000000000000000000
χ834-4-44-200-440022-22-2-2200002i3−2i32i−2i−2i2i2i−2i−2i2i00000000−2i32i32ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ2200000000000000000000000000
χ844-4-44-200-440022-22-2-2200002i3−2i3−2i2i2i−2i−2i2i2i−2i00000000−2i32i3−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ2200000000000000000000000000

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