Finite Group Databasebeta

← Group #10693072

Character table — Group #10693072

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order122222344444466666662244444444412121212121212122244666666121212121212121212121212888888888888888844121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1111-1-1-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111-1-1111-1-1-1-1-1-1111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ711111111111111111111-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ811111111111111111111-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111111-1-1-1-1-1-111111111111-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1i−ii−i
χ101111111-1-1-1-1-1-111111111111-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1−ii−ii
χ111111111-1-1-1-1-1-111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−i-11-1-111−ii−ii
χ121111111-1-1-1-1-1-111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii-11-1-111i−ii−i
χ131111111-1-1-1-1-1-11111111-1-111-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-111i−i−ii
χ141111111-1-1-1-1-1-11111111-1-111-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-111−iii−i
χ151111111-1-1-1-1-1-11111111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111iiii−i−i−i−i−i−i−i−iiiii1-111-1-1−iii−i
χ161111111-1-1-1-1-1-11111111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1i−i−ii
χ1722222222222-2-2222222222-2-2-222-2-2-2-2-2-2-2-222220000220000-2-222-2-2-2-2000000000000000000000000000000
χ1822222222222-2-22222222-2-2-2-2-2-2-22222-2-2-2-222220000-2-20000-2-2-2-22222000000000000000000000000000000
χ192222222-2-2-2-222222222222-2-22-2-222-2-22222-2-2-2-20000220000-2-2-2-222-2-2000000000000000000000000000000
χ202222222-2-2-2-2222222222-2-2-2-2222-2-2222222-2-2-2-20000-2-20000-2-222-2-222000000000000000000000000000000
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
χ22222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-1-1-1-1-1-111110000000000000000-2-211110000
χ23222222-1222222-1-1-1-1-1-1-1-2-2222-2-2-2-2-2-2-1-1-1-1-1-1-1-1222211-1-1-1-1-1-1111111-1-1-1-10000000000000000-2-211110000
χ24222222-1222222-1-1-1-1-1-1-1-2-2222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2111111-1-11111111111000000000000000022-1-1-1-10000
χ25222222-12222-2-2-1-1-1-1-1-1-122-2-2-222-2-2-2-21111-1-1-1-10000-1-1−i3−i3i3i311-1-11111−i3−i3i3i3000000000000000000−i3i3−i3i30000
χ26222222-12222-2-2-1-1-1-1-1-1-122-2-2-222-2-2-2-21111-1-1-1-10000-1-1i3i3−i3−i311-1-11111i3i3−i3−i3000000000000000000i3−i3i3−i30000
χ27222222-12222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-222221111-1-1-1-1000011−i3−i3i3i31111-1-1-1-1−i3−i3i3i3000000000000000000i3−i3i3−i30000
χ28222222-12222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-222221111-1-1-1-1000011i3i3−i3−i31111-1-1-1-1i3i3−i3−i3000000000000000000−i3i3−i3i30000
χ29222222-1-2-2-2-222-1-1-1-1-1-1-122-2-22-2-222-2-2-1-1-1-111110000-1-1−i3−i3i3i31111-1-111i3i3−i3−i3000000000000000000−i3i3i3−i30000
χ30222222-1-2-2-2-222-1-1-1-1-1-1-122-2-22-2-222-2-2-1-1-1-111110000-1-1i3i3−i3−i31111-1-111−i3−i3i3i3000000000000000000i3−i3−i3i30000
χ31222222-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2222-2-222-1-1-1-11111000011−i3−i3i3i311-1-111-1-1i3i3−i3−i3000000000000000000i3−i3−i3i30000
χ32222222-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2222-2-222-1-1-1-11111000011i3i3−i3−i311-1-111-1-1−i3−i3i3i3000000000000000000−i3i3i3−i30000
χ33222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-2221111111122-2-2-1-1-1-1-1-1-1-11111-1-1111100000000000000002-2-1-1110000
χ34222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-22211111111-2-222-1-11111-1-11111-1-1-1-1-1-10000000000000000-2211-1-10000
χ35222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2-222-22222-2-21111111122-2-211-1-1-1-1-1-1-1-1-1-11111110000000000000000-2211-1-10000
χ36222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2-222-22222-2-211111111-2-222111111-1-1-1-1-1-111-1-1-1-100000000000000002-2-1-1110000
χ372222-2-2222-2-222-2-2-2-2222002-2-200000022-2-222-2-200000000002-200000000000000000022-2-222-2-20000000000
χ382222-2-2222-2-222-2-2-2-2222002-2-200000022-2-222-2-200000000002-2000000000000000000-2-222-2-2220000000000
χ392222-2-2222-2-2-2-2-2-2-2-222200-222000000-2-22222-2-20000000000-2200000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ402222-2-2222-2-2-2-2-2-2-2-222200-222000000-2-22222-2-20000000000-220000000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ412222-2-22-2-22222-2-2-2-222200-22-200000022-2-2-2-2220000000000-22000000000022-2-2-2-222000000000000000000
χ422222-2-22-2-22222-2-2-2-222200-22-200000022-2-2-2-2220000000000-220000000000-2-22222-2-2000000000000000000
χ432222-2-22-2-222-2-2-2-2-2-2222002-22000000-2-222-2-22200000000002-20000000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ442222-2-22-2-222-2-2-2-2-2-2222002-22000000-2-222-2-22200000000002-2000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ4522-2-22-222i−2i2i−2i0022-2-22-2-200000002-22i−2i00002i−2i2i−2i000000000000002-22i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ4622-2-22-222i−2i2i−2i0022-2-22-2-200000002-22i−2i00002i−2i2i−2i000000000000002-22i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ4722-2-22-222i−2i2i−2i0022-2-22-2-20000000-22−2i2i00002i−2i2i−2i00000000000000-22−2i2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ4822-2-22-222i−2i2i−2i0022-2-22-2-20000000-22−2i2i00002i−2i2i−2i00000000000000-22−2i2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ4922-2-22-22−2i2i−2i2i0022-2-22-2-200000002-2−2i2i0000−2i2i−2i2i000000000000002-2−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ5022-2-22-22−2i2i−2i2i0022-2-22-2-200000002-2−2i2i0000−2i2i−2i2i000000000000002-2−2i2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ5122-2-22-22−2i2i−2i2i0022-2-22-2-20000000-222i−2i0000−2i2i−2i2i00000000000000-222i−2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ5222-2-22-22−2i2i−2i2i0022-2-22-2-20000000-222i−2i0000−2i2i−2i2i00000000000000-222i−2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ5322-2-2-2222i−2i−2i2i00-2-2222-2-22-20002i−2i000000002i−2i−2i2i00002-20000002i−2i000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ5422-2-2-2222i−2i−2i2i00-2-2222-2-22-20002i−2i000000002i−2i−2i2i00002-20000002i−2i00000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ5522-2-2-2222i−2i−2i2i00-2-2222-2-2-22000−2i2i000000002i−2i−2i2i0000-22000000−2i2i000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ5622-2-2-2222i−2i−2i2i00-2-2222-2-2-22000−2i2i000000002i−2i−2i2i0000-22000000−2i2i00000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ5722-2-2-222−2i2i2i−2i00-2-2222-2-22-2000−2i2i00000000−2i2i2i−2i00002-2000000−2i2i000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ5822-2-2-222−2i2i2i−2i00-2-2222-2-22-2000−2i2i00000000−2i2i2i−2i00002-2000000−2i2i00000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ5922-2-2-222−2i2i2i−2i00-2-2222-2-2-220002i−2i00000000−2i2i2i−2i0000-220000002i−2i000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ6022-2-2-222−2i2i2i−2i00-2-2222-2-2-220002i−2i00000000−2i2i2i−2i0000-220000002i−2i00000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ614444-4-4-244-4-4442222-2-2-2004-4-4000000-2-222-2-2220000000000-22000000000000000000000000000000000000
χ624444-4-4-244-4-4-4-42222-2-2-200-44400000022-2-2-2-22200000000002-2000000000000000000000000000000000000
χ634444-4-4-2-4-444442222-2-2-200-44-4000000-2-22222-2-200000000002-2000000000000000000000000000000000000
χ644444-4-4-2-4-444-4-42222-2-2-2004-4400000022-2-222-2-20000000000-22000000000000000000000000000000000000
χ6544-4-44-4-24i−4i4i−4i00-2-222-22200000004-44i−4i0000−2i2i−2i2i00000000000000-22−2i2i000000000000000000000000000000
χ6644-4-44-4-24i−4i4i−4i00-2-222-2220000000-44−4i4i0000−2i2i−2i2i000000000000002-22i−2i000000000000000000000000000000
χ6744-4-44-4-2−4i4i−4i4i00-2-222-22200000004-4−4i4i00002i−2i2i−2i00000000000000-222i−2i000000000000000000000000000000
χ6844-4-44-4-2−4i4i−4i4i00-2-222-2220000000-444i−4i00002i−2i2i−2i000000000000002-2−2i2i000000000000000000000000000000
χ6944-4-4-44-24i−4i−4i4i0022-2-2-2224-40004i−4i00000000−2i2i2i−2i0000-22000000−2i2i0000000000000000000000000000000000
χ7044-4-4-44-24i−4i−4i4i0022-2-2-222-44000−4i4i00000000−2i2i2i−2i00002-20000002i−2i0000000000000000000000000000000000
χ7144-4-4-44-2−4i4i4i−4i0022-2-2-2224-4000−4i4i000000002i−2i−2i2i0000-220000002i−2i0000000000000000000000000000000000
χ7244-4-4-44-2−4i4i4i−4i0022-2-2-222-440004i−4i000000002i−2i−2i2i00002-2000000−2i2i0000000000000000000000000000000000
χ734-44-400400004i−4i0000-44-4000000000004i−4i0000002-22i−2i002-22-2000000002i−2i2i−2i00000000000000000000000000
χ744-44-400400004i−4i0000-44-4000000000004i−4i000000-22−2i2i00-22-2200000000−2i2i−2i2i00000000000000000000000000
χ754-44-40040000−4i4i0000-44-400000000000−4i4i0000002-2−2i2i002-22-200000000−2i2i−2i2i00000000000000000000000000
χ764-44-40040000−4i4i0000-44-400000000000−4i4i000000-222i−2i00-22-22000000002i−2i2i−2i00000000000000000000000000
χ774-44-400-200004i−4i−2i32i3−2i32i32-2200000000000−2i2i23−2300002-22i−2i00−1−i31+i3−1+i31−i3000000002ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ784-44-400-200004i−4i−2i32i3−2i32i32-2200000000000−2i2i23−230000-22−2i2i001+i3−1−i31−i3−1+i300000000−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ794-44-400-200004i−4i2i3−2i32i3−2i32-2200000000000−2i2i−232300002-22i−2i00−1+i31−i3−1−i31+i3000000002ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ804-44-400-200004i−4i2i3−2i32i3−2i32-2200000000000−2i2i−23230000-22−2i2i001−i3−1+i31+i3−1−i300000000−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ814-44-400-20000−4i4i−2i32i3−2i32i32-22000000000002i−2i−232300002-2−2i2i00−1−i31+i3−1+i31−i300000000−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ824-44-400-20000−4i4i−2i32i3−2i32i32-22000000000002i−2i−23230000-222i−2i001+i3−1−i31−i3−1+i3000000002ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ834-44-400-20000−4i4i2i3−2i32i3−2i32-22000000000002i−2i23−2300002-2−2i2i00−1+i31−i3−1−i31+i300000000−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ844-44-400-20000−4i4i2i3−2i32i3−2i32-22000000000002i−2i23−230000-222i−2i001−i3−1+i31+i3−1−i3000000002ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ858-8-880080000000000-8-880000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-4000000−4i34i34i3−4i344-40000000000000000000000000000000000000000000000000000000000000000000
χ878-8-8800-40000004i3−4i3−4i34i344-40000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.