Finite Group Databasebeta

← Group #10687354

Character table — Group #10687354

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222222224444444488888888888888888888888888888888888888242424242424242448484848
order122222344446666666121212121212121244444444448888888812121212121212121212121224242424242424242424242424242424224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ91111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1ii−i−iii−i−i11-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−i
χ101111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1ii−i−iii−i−i11-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii
χ111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−iii−i−iii11-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii
χ121111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−iii−i−iii11-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−i
χ131111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111ii−i−i−i−iii11-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-111-1-11i−i−ii
χ141111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111ii−i−i−i−iii11-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-111-1-111-1−iii−i
χ151111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111−i−iiiii−i−i11-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-111-1-11−iii−i
χ161111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111−i−iiiii−i−i11-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-111-1-111-1i−i−ii
χ1722222222222222222222222222-2-222-2-2-2-22-200000000-2-2-2-222-2-222-2-20000000000000000000000000000
χ1822222222222222222222222222-2-2-2-222-2-2-2200000000-2-2-2-2-2-222-2-2220000000000000000000000000000
χ192222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-222-2-222-2200000000-2-22222-2-2-2-2220000000000000000000000000000
χ202222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-222222-200000000-2-222-2-22222-2-20000000000000000000000000000
χ21222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000
χ23222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000
χ24222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-1000000000000
χ25222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-22-2000000001111-1-111-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ26222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-22-2000000001111-1-111-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000
χ27222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2200000000111111-1-111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000
χ28222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2200000000111111-1-111-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000
χ29222222-1-2-2-2-2-1-1-1-1-1-1-111111111222222-2-2-2-22i2i−2i−2i2i2i−2i−2i-1-111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii000000000000
χ30222222-1-2-2-2-2-1-1-1-1-1-1-111111111222222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-1-111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i000000000000
χ31222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i-1-1111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ32222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i-1-1111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000
χ33222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-222-220000000011-1-1-1-11111-1-133−3−3−3−33333−3−3−3−333000000000000
χ34222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-222-220000000011-1-1-1-11111-1-1−3−33333−3−3−3−33333−3−3000000000000
χ35222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-222222-20000000011-1-111-1-1-1-11133−3−3−3−333−3−33333−3−3000000000000
χ36222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-222222-20000000011-1-111-1-1-1-111−3−33333−3−333−3−3−3−333000000000000
χ372222-2-222-2-22-2-2-2-222222-2-2-2-2222-200002-200000000002-22-2000000000000000000000000002200-2-20000
χ382222-2-222-2-22-2-2-2-222222-2-2-2-2222-200002-200000000002-22-200000000000000000000000000-2-200220000
χ392222-2-222-2-22-2-2-2-222222-2-2-2-222-220000-220000000000-22-220000000000000000000000002200-2-2000000
χ402222-2-222-2-22-2-2-2-222222-2-2-2-222-220000-220000000000-22-22000000000000000000000000-2-20022000000
χ412222-2-22-222-2-2-2-2-2222-2-22222-2-22-20000-2200000000002-2-22000000000000000000000000002-200-220000
χ422222-2-22-222-2-2-2-2-2222-2-22222-2-22-20000-2200000000002-2-2200000000000000000000000000-22002-20000
χ432222-2-22-222-2-2-2-2-2222-2-22222-2-2-2200002-20000000000-222-20000000000000000000000002-200-22000000
χ442222-2-22-222-2-2-2-2-2222-2-22222-2-2-2200002-20000000000-222-2000000000000000000000000-22002-2000000
χ454444-4-4-24-4-442222-2-2-2-2-22222-2-24-400004-40000000000-22-22000000000000000000000000000000000000
χ464444-4-4-24-4-442222-2-2-2-2-22222-2-2-440000-4400000000002-22-2000000000000000000000000000000000000
χ474444-4-4-2-444-42222-2-2-222-2-2-2-2224-40000-440000000000-222-2000000000000000000000000000000000000
χ484444-4-4-2-444-42222-2-2-222-2-2-2-222-4400004-400000000002-2-22000000000000000000000000000000000000
χ4944-4-4004400-400004-4-4440000-4-400000000002-22-200000000000000002-22-22-22-200000000000000000000
χ5044-4-4004400-400004-4-4440000-4-40000000000-22-220000000000000000-22-22-22-2200000000000000000000
χ5144-4-4004-400400004-4-4-4-400004400000000002i−2i−2i2i00000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ5244-4-4004-400400004-4-4-4-40000440000000000−2i2i2i−2i0000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ5344-4-400-2400-4−2i3−2i32i32i3-222-2-2−2i3−2i32i32i32200000000002-22-20000000000000000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i300000000000000000000
χ5444-4-400-2400-4−2i3−2i32i32i3-222-2-2−2i3−2i32i32i3220000000000-22-2200000000000000001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i300000000000000000000
χ5544-4-400-2400-42i32i3−2i3−2i3-222-2-22i32i3−2i3−2i32200000000002-22-20000000000000000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i300000000000000000000
χ5644-4-400-2400-42i32i3−2i3−2i3-222-2-22i32i3−2i3−2i3220000000000-22-2200000000000000001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i300000000000000000000
χ5744-4-400-2-4004−2i3−2i32i32i3-222222i32i3−2i3−2i3-2-200000000002i−2i−2i2i00000000000000002ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ1400000000000000000000
χ5844-4-400-2-4004−2i3−2i32i32i3-222222i32i3−2i3−2i3-2-20000000000−2i2i2i−2i0000000000000000−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ1400000000000000000000
χ5944-4-400-2-40042i32i3−2i3−2i3-22222−2i3−2i32i32i3-2-200000000002i−2i−2i2i00000000000000002ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ2200000000000000000000
χ6044-4-400-2-40042i32i3−2i3−2i3-22222−2i3−2i32i32i3-2-20000000000−2i2i2i−2i0000000000000000−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ2200000000000000000000
χ614-44-400404i−4i00000-44-4004i−4i4i−4i00000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000
χ624-44-400404i−4i00000-44-4004i−4i4i−4i0000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000
χ634-44-40040−4i4i00000-44-400−4i4i−4i4i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000
χ644-44-40040−4i4i00000-44-400−4i4i−4i4i00000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000
χ654-44-400-204i−4i0−2i32i3−2i32i32-2223−23−2i2i−2i2i23−23000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000−2ζ72ζ7−2ζ232ζ232ζ13−2ζ132ζ5−2ζ5000000000000
χ664-44-400-204i−4i0−2i32i3−2i32i32-2223−23−2i2i−2i2i23−2300000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000002ζ7−2ζ72ζ23−2ζ23−2ζ132ζ13−2ζ52ζ5000000000000
χ674-44-400-204i−4i02i3−2i32i3−2i32-22−2323−2i2i−2i2i−2323000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000−2ζ232ζ23−2ζ72ζ72ζ5−2ζ52ζ13−2ζ13000000000000
χ684-44-400-204i−4i02i3−2i32i3−2i32-22−2323−2i2i−2i2i−232300000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000002ζ23−2ζ232ζ7−2ζ7−2ζ52ζ5−2ζ132ζ13000000000000
χ694-44-400-20−4i4i0−2i32i3−2i32i32-22−23232i−2i2i−2i−232300000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000002ζ13−2ζ132ζ5−2ζ5−2ζ72ζ7−2ζ232ζ23000000000000
χ704-44-400-20−4i4i0−2i32i3−2i32i32-22−23232i−2i2i−2i−2323000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000−2ζ132ζ13−2ζ52ζ52ζ7−2ζ72ζ23−2ζ23000000000000
χ714-44-400-20−4i4i02i3−2i32i3−2i32-2223−232i−2i2i−2i23−2300000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000002ζ5−2ζ52ζ13−2ζ13−2ζ232ζ23−2ζ72ζ7000000000000
χ724-44-400-20−4i4i02i3−2i32i3−2i32-2223−232i−2i2i−2i23−23000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000−2ζ52ζ5−2ζ132ζ132ζ23−2ζ232ζ7−2ζ7000000000000
χ734-4-444-4400004-4-44-4-4400000000004i−4i0000000000000000004i−4i0000000000000000000000000000000000
χ744-4-444-4400004-4-44-4-440000000000−4i4i000000000000000000−4i4i0000000000000000000000000000000000
χ754-4-444-4-20000-222-222-223−2323−23−2323−2323004i−4i000000000000000000−2i2i00−2i32i3000000000000000000000000000000
χ764-4-444-4-20000-222-222-223−2323−23−2323−232300−4i4i0000000000000000002i−2i002i3−2i3000000000000000000000000000000
χ774-4-444-4-20000-222-222-2−2323−232323−2323−23004i−4i000000000000000000−2i2i002i3−2i3000000000000000000000000000000
χ784-4-444-4-20000-222-222-2−2323−232323−2323−2300−4i4i0000000000000000002i−2i00−2i32i3000000000000000000000000000000
χ794-4-44-4440000-444-4-4-440000000000004i−4i0000000000000000004i−4i00000000000000000000000000000000
χ804-4-44-4440000-444-4-4-44000000000000−4i4i000000000000000000−4i4i00000000000000000000000000000000
χ814-4-44-44-200002-2-2222-223−23−232323−23−232300004i−4i000000000000000000−2i2i00−2i32i30000000000000000000000000000
χ824-4-44-44-200002-2-2222-223−23−232323−23−23230000−4i4i0000000000000000002i−2i002i3−2i30000000000000000000000000000
χ834-4-44-44-200002-2-2222-2−232323−23−232323−2300004i−4i000000000000000000−2i2i002i3−2i30000000000000000000000000000
χ844-4-44-44-200002-2-2222-2−232323−23−232323−230000−4i4i0000000000000000002i−2i00−2i32i30000000000000000000000000000

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