Finite Group Databasebeta

← Group #10693032

Character table — Group #10693032

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order122222344444466666664444444444412121212121212124444121212121212121212121212121212121212888888888888888844121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ7111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ8111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111111-1-1-1-1-1-11111111-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1i−ii−i
χ101111111-1-1-1-1-1-11111111-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1−ii−ii
χ111111111-1-1-1-1-1-11111111-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111iiii−i−i−i−iiiii−i−i−i−i-11-1-111−ii−ii
χ121111111-1-1-1-1-1-11111111-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111−i−i−i−iiiii−i−i−i−iiiii-11-1-111i−ii−i
χ131111111-1-1-1-1-1-11111111-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-111i−i−ii
χ141111111-1-1-1-1-1-11111111-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-111−iii−i
χ151111111-1-1-1-1-1-11111111-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1111111iiii−i−i−i−i−i−i−i−iiiii1-111-1-1−iii−i
χ161111111-1-1-1-1-1-11111111-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1111111−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1i−i−ii
χ1722222222222-2-22222222-22222-2-2-2-2-2-22222-2-2-2-2000022220000-2-2-2-2-2-2000000000000000000000000000000
χ1822222222222-2-22222222-2-2-2-2-2-2-222222222-2-2-2-20000-2-2-2-20000-2-22222000000000000000000000000000000
χ192222222-2-2-2-2222222222222-2-2-2-2-2-222-2-2-2-22222000022-2-20000-2-2-2-222000000000000000000000000000000
χ202222222-2-2-2-22222222222-2-222-2-222-2-2-2-2-2-222220000-2-2220000-2-222-2-2000000000000000000000000000000
χ21222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ22222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111-1-1-1-1-1-111110000000000000000-2-211110000
χ23222222-1222222-1-1-1-1-1-1-12-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-122221111-1-1-1-1-1-11111-1-1-1-10000000000000000-2-211110000
χ24222222-1222222-1-1-1-1-1-1-12-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-211111111-1-111111111000000000000000022-1-1-1-10000
χ25222222-12222-2-2-1-1-1-1-1-1-1-22222-2-2-2-2-2-2-1-1-1-111110000-1-1-1-1−i3−i3i3i3111111−i3−i3i3i3000000000000000000−i3i3−i3i30000
χ26222222-12222-2-2-1-1-1-1-1-1-1-22222-2-2-2-2-2-2-1-1-1-111110000-1-1-1-1i3i3−i3−i3111111i3i3−i3−i3000000000000000000i3−i3i3−i30000
χ27222222-12222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-22222-1-1-1-1111100001111−i3−i3i3i311-1-1-1-1−i3−i3i3i3000000000000000000i3−i3i3−i30000
χ28222222-12222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-22222-1-1-1-1111100001111i3i3−i3−i311-1-1-1-1i3i3−i3−i3000000000000000000−i3i3−i3i30000
χ29222222-1-2-2-2-222-1-1-1-1-1-1-1222-2-2-2-2-2-2221111-1-1-1-10000-1-111−i3−i3i3i31111-1-1i3i3−i3−i3000000000000000000−i3i3i3−i30000
χ30222222-1-2-2-2-222-1-1-1-1-1-1-1222-2-2-2-2-2-2221111-1-1-1-10000-1-111i3i3−i3−i31111-1-1−i3−i3i3i3000000000000000000i3−i3−i3i30000
χ31222222-1-2-2-2-222-1-1-1-1-1-1-12-2-222-2-222-2-21111-1-1-1-1000011-1-1−i3−i3i3i311-1-111i3i3−i3−i3000000000000000000i3−i3−i3i30000
χ32222222-1-2-2-2-222-1-1-1-1-1-1-12-2-222-2-222-2-21111-1-1-1-1000011-1-1i3i3−i3−i311-1-111−i3−i3i3i3000000000000000000−i3i3i3−i30000
χ33222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-222-2-22222-2-21111111122-2-2-1-111-1-1-1-1-1-1-1-111111100000000000000002-2-1-1110000
χ34222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-222-2-22222-2-211111111-2-222-1-1111111-1-1-1-111-1-1-1-10000000000000000-2211-1-10000
χ35222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2-22222-2-2221111111122-2-211-1-1-1-1-1-1-1-111-1-111110000000000000000-2211-1-10000
χ36222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2-22222-2-22211111111-2-22211-1-11111-1-111-1-1-1-1-1-100000000000000002-2-1-1110000
χ372222-2-222-22-222-2-2-2-2222-200002-2000022-2-222-2-20000000000002-2000000000000000022-2-222-2-20000000000
χ382222-2-222-22-222-2-2-2-2222-200002-2000022-2-222-2-20000000000002-20000000000000000-2-222-2-2220000000000
χ392222-2-222-22-2-2-2-2-2-2-222220000-22000022-2-2-2-222000000000000-22000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ402222-2-222-22-2-2-2-2-2-2-222220000-22000022-2-2-2-222000000000000-2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ412222-2-22-22-2222-2-2-2-2222-20000-220000-2-22222-2-2000000000000-220000000022-2-2-2-222000000000000000000
χ422222-2-22-22-2222-2-2-2-2222-20000-220000-2-22222-2-2000000000000-2200000000-2-22222-2-2000000000000000000
χ432222-2-22-22-22-2-2-2-2-2-2222200002-20000-2-222-2-2220000000000002-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ442222-2-22-22-22-2-2-2-2-2-2222200002-20000-2-222-2-2220000000000002-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ4522-2-22-2222-2-20022-2-22-2-202-22-20000002-22-2000000002-22-2000000000000002−22−22−22−22−22−22−22−20000000000
χ4622-2-22-2222-2-20022-2-22-2-202-22-20000002-22-2000000002-22-200000000000000−22−22−22−22−22−22−22−220000000000
χ4722-2-22-2222-2-20022-2-22-2-20-22-220000002-22-200000000-22-22000000000000002−22−22−22−2−22−22−22−220000000000
χ4822-2-22-2222-2-20022-2-22-2-20-22-220000002-22-200000000-22-2200000000000000−22−22−22−222−22−22−22−20000000000
χ4922-2-22-22-2-2220022-2-22-2-202-2-22000000-22-22000000002-2-2200000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ5022-2-22-22-2-2220022-2-22-2-202-2-22000000-22-22000000002-2-2200000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ5122-2-22-22-2-2220022-2-22-2-20-222-2000000-22-2200000000-222-200000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ5222-2-22-22-2-2220022-2-22-2-20-222-2000000-22-2200000000-222-200000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ5322-2-2-2222-2-2200-2-2222-2-200000002i−2i2i−2i2-2-220000000000000000002i−2i2i−2i0000−i2i2i2−i2−i2i2i2−i22−2−222−2−220000000000
χ5422-2-2-2222-2-2200-2-2222-2-200000002i−2i2i−2i2-2-220000000000000000002i−2i2i−2i0000i2−i2−i2i2i2−i2−i2i2−222−2−222−20000000000
χ5522-2-2-2222-2-2200-2-2222-2-20000000−2i2i−2i2i2-2-22000000000000000000−2i2i−2i2i0000−i2i2i2−i2−i2i2i2−i2−222−2−222−20000000000
χ5622-2-2-2222-2-2200-2-2222-2-20000000−2i2i−2i2i2-2-22000000000000000000−2i2i−2i2i0000i2−i2−i2i2i2−i2−i2i22−2−222−2−220000000000
χ5722-2-2-222-222-200-2-2222-2-200000002i−2i−2i2i-222-20000000000000000002i−2i−2i2i00002−2−22−222−2i2−i2−i2i2−i2i2i2−i20000000000
χ5822-2-2-222-222-200-2-2222-2-200000002i−2i−2i2i-222-20000000000000000002i−2i−2i2i0000−222−22−2−22−i2i2i2−i2i2−i2−i2i20000000000
χ5922-2-2-222-222-200-2-2222-2-20000000−2i2i2i−2i-222-2000000000000000000−2i2i2i−2i00002−2−22−222−2−i2i2i2−i2i2−i2−i2i20000000000
χ6022-2-2-222-222-200-2-2222-2-20000000−2i2i2i−2i-222-2000000000000000000−2i2i2i−2i0000−222−22−2−22i2−i2−i2i2−i2i2i2−i20000000000
χ614444-4-4-24-44-4442222-2-2-2-400004-40000-2-222-2-222000000000000-220000000000000000000000000000000000
χ624444-4-4-24-44-4-4-42222-2-2-240000-440000-2-22222-2-20000000000002-20000000000000000000000000000000000
χ634444-4-4-2-44-44442222-2-2-2-40000-44000022-2-2-2-2220000000000002-20000000000000000000000000000000000
χ644444-4-4-2-44-44-4-42222-2-2-2400004-4000022-2-222-2-2000000000000-220000000000000000000000000000000000
χ6544-4-44-4-244-4-400-2-222-22204-44-4000000-22-2200000000-22-220000000000000000000000000000000000000000
χ6644-4-44-4-244-4-400-2-222-2220-44-44000000-22-22000000002-22-20000000000000000000000000000000000000000
χ6744-4-44-4-2-4-44400-2-222-22204-4-440000002-22-200000000-222-20000000000000000000000000000000000000000
χ6844-4-44-4-2-4-44400-2-222-2220-444-40000002-22-2000000002-2-220000000000000000000000000000000000000000
χ6944-4-4-44-24-4-440022-2-2-22200000004i−4i4i−4i-222-2000000000000000000−2i2i−2i2i000000000000000000000000000000
χ7044-4-4-44-24-4-440022-2-2-2220000000−4i4i−4i4i-222-20000000000000000002i−2i2i−2i000000000000000000000000000000
χ7144-4-4-44-2-444-40022-2-2-22200000004i−4i−4i4i2-2-22000000000000000000−2i2i2i−2i000000000000000000000000000000
χ7244-4-4-44-2-444-40022-2-2-2220000000−4i4i4i−4i2-2-220000000000000000002i−2i−2i2i000000000000000000000000000000
χ734-4-4400400004i−4i0000-4-440000000000000004i−4i002i−2i2-200002i−2i2i−2i0000002-22-200000000000000000000000000
χ744-4-4400400004i−4i0000-4-440000000000000004i−4i00−2i2i-220000−2i2i−2i2i000000-22-2200000000000000000000000000
χ754-4-440040000−4i4i0000-4-44000000000000000−4i4i002i−2i-2200002i−2i2i−2i000000-22-2200000000000000000000000000
χ764-4-440040000−4i4i0000-4-44000000000000000−4i4i00−2i2i2-20000−2i2i−2i2i0000002-22-200000000000000000000000000
χ774-4-4400-200004i−4i−2i32i3−2i32i322-2000000000000000−2i2i23−232i−2i2-200002ζ14−2ζ142ζ22−2ζ22000000−1−i31+i3−1+i31−i300000000000000000000000000
χ784-4-4400-200004i−4i−2i32i3−2i32i322-2000000000000000−2i2i23−23−2i2i-220000−2ζ142ζ14−2ζ222ζ220000001+i3−1−i31−i3−1+i300000000000000000000000000
χ794-4-4400-200004i−4i2i3−2i32i3−2i322-2000000000000000−2i2i−23232i−2i2-200002ζ22−2ζ222ζ14−2ζ14000000−1+i31−i3−1−i31+i300000000000000000000000000
χ804-4-4400-200004i−4i2i3−2i32i3−2i322-2000000000000000−2i2i−2323−2i2i-220000−2ζ222ζ22−2ζ142ζ140000001−i3−1+i31+i3−1−i300000000000000000000000000
χ814-4-4400-20000−4i4i−2i32i3−2i32i322-20000000000000002i−2i−23232i−2i-2200002ζ14−2ζ142ζ22−2ζ220000001+i3−1−i31−i3−1+i300000000000000000000000000
χ824-4-4400-20000−4i4i−2i32i3−2i32i322-20000000000000002i−2i−2323−2i2i2-20000−2ζ142ζ14−2ζ222ζ22000000−1−i31+i3−1+i31−i300000000000000000000000000
χ834-4-4400-20000−4i4i2i3−2i32i3−2i322-20000000000000002i−2i23−232i−2i-2200002ζ22−2ζ222ζ14−2ζ140000001−i3−1+i31+i3−1−i300000000000000000000000000
χ844-4-4400-20000−4i4i2i3−2i32i3−2i322-20000000000000002i−2i23−23−2i2i2-20000−2ζ222ζ22−2ζ142ζ14000000−1+i31−i3−1−i31+i300000000000000000000000000
χ858-88-80080000000000-88-80000000000000000000000000000000000000000000000000000000000000000000
χ868-88-800-4000000−4i34i34i3−4i34-440000000000000000000000000000000000000000000000000000000000000000000
χ878-88-800-40000004i3−4i3−4i34i34-440000000000000000000000000000000000000000000000000000000000000000000

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