Finite Group Databasebeta

← Group #10692997

Character table — Group #10692997

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order1222222234444666666622222444444666612121212444466661212121212121212121212121212444444444444444444121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ7111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ8111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ9111111-1-11-1-1-1-11111111-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1i−ii−i
χ10111111-1-11-1-1-1-11111111-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1−ii−ii
χ11111111-1-11-1-1-1-11111111-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111iiii−i−i−i−iiiii−i−i−i−i-11-1-111−ii−ii
χ12111111-1-11-1-1-1-11111111-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111−i−i−i−iiiii−i−i−i−iiiii-11-1-111i−ii−i
χ13111111-1-11-1-1-1-11111111-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-111i−i−ii
χ14111111-1-11-1-1-1-11111111-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-111−iii−i
χ15111111-1-11-1-1-1-11111111-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii1-111-1-1−iii−i
χ16111111-1-11-1-1-1-11111111-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1i−i−ii
χ17222222222-2-2-2-2222222222222-2-2-2-2-2-22222-2-2-2-200002222-2-20000-2-2-2-2000000000000000000000000000000
χ18222222222-2-2-2-222222222-2-2-2-2-2-222222222-2-2-2-20000-2-2-2-2-2-200002222000000000000000000000000000000
χ1922222222-12222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ2022222222-12222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-11111-1-1-1-111110000000000000000-2-211110000
χ2122222222-12222-1-1-1-1-1-1-12-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-122221111-1-1-1-1-1-11111-1-1-1-10000000000000000-2-211110000
χ2222222222-12222-1-1-1-1-1-1-12-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-21111-1-1111111111111000000000000000022-1-1-1-10000
χ2322222222-1-2-2-2-2-1-1-1-1-1-1-122222-2-2-2-2-2-2-1-1-1-111110000-1-1-1-111−i3−i3i3i31111−i3−i3i3i3000000000000000000−i3i3−i3i30000
χ2422222222-1-2-2-2-2-1-1-1-1-1-1-122222-2-2-2-2-2-2-1-1-1-111110000-1-1-1-111i3i3−i3−i31111i3i3−i3−i3000000000000000000i3−i3i3−i30000
χ2522222222-1-2-2-2-2-1-1-1-1-1-1-12-2-2-2-2-2-22222-1-1-1-111110000111111−i3−i3i3i3-1-1-1-1−i3−i3i3i3000000000000000000i3−i3i3−i30000
χ2622222222-1-2-2-2-2-1-1-1-1-1-1-12-2-2-2-2-2-22222-1-1-1-111110000111111i3i3−i3−i3-1-1-1-1i3i3−i3−i3000000000000000000−i3i3−i3i30000
χ27222222-2-2222222222222-222-2-2-2-2-2-222-2-2-2-22222000022-2-2-2-20000-2-222000000000000000000000000000000
χ28222222-2-2222222222222-2-2-222-2-222-2-2-2-2-2-222220000-2-222-2-2000022-2-2000000000000000000000000000000
χ29222222-2-2-12222-1-1-1-1-1-1-1-222-2-2-2-2-2-2221111-1-1-1-10000-1-11111−i3−i3i3i311-1-1i3i3−i3−i3000000000000000000−i3i3i3−i30000
χ30222222-2-2-12222-1-1-1-1-1-1-1-222-2-2-2-2-2-2221111-1-1-1-10000-1-11111i3i3−i3−i311-1-1−i3−i3i3i3000000000000000000i3−i3−i3i30000
χ31222222-2-2-12222-1-1-1-1-1-1-1-2-2-222-2-222-2-21111-1-1-1-1000011-1-111−i3−i3i3i3-1-111i3i3−i3−i3000000000000000000i3−i3−i3i30000
χ32222222-2-2-12222-1-1-1-1-1-1-1-2-2-222-2-222-2-21111-1-1-1-1000011-1-111i3i3−i3−i3-1-111−i3−i3i3i3000000000000000000−i3i3i3−i30000
χ33222222-2-2-1-2-2-2-2-1-1-1-1-1-1-1-222-2-22222-2-21111111122-2-2-1-111-1-1-1-1-1-1-1-111111100000000000000002-2-1-1110000
χ34222222-2-2-1-2-2-2-2-1-1-1-1-1-1-1-222-2-22222-2-211111111-2-222-1-111-1-11111-1-111-1-1-1-10000000000000000-2211-1-10000
χ35222222-2-2-1-2-2-2-2-1-1-1-1-1-1-1-2-2-22222-2-2221111111122-2-211-1-1-1-1-1-1-1-111-1-111110000000000000000-2211-1-10000
χ36222222-2-2-1-2-2-2-2-1-1-1-1-1-1-1-2-2-22222-2-22211111111-2-22211-1-1-1-1111111-1-1-1-1-1-100000000000000002-2-1-1110000
χ372222-2-222222-2-2-2-2-2-2222-200002-2000022-2-222-2-2000000002-20000000000000000000022-2-222-2-20000000000
χ382222-2-222222-2-2-2-2-2-2222-200002-2000022-2-222-2-2000000002-200000000000000000000-2-222-2-2220000000000
χ392222-2-2222-2-222-2-2-2-2222-20000-22000022-2-2-2-22200000000-2200000000000022-2-222-2-2000000000000000000
χ402222-2-2222-2-222-2-2-2-2222-20000-22000022-2-2-2-22200000000-22000000000000-2-222-2-222000000000000000000
χ412222-2-2-2-2222-2-2-2-2-2-222220000-220000-2-22222-2-200000000-220000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ422222-2-2-2-2222-2-2-2-2-2-222220000-220000-2-22222-2-200000000-22000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ432222-2-2-2-22-2-222-2-2-2-2222200002-20000-2-222-2-222000000002-2000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ442222-2-2-2-22-2-222-2-2-2-2222200002-20000-2-222-2-222000000002-200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ4522-2-22-20022i−2i2i−2i22-2-22-2-20002-2002i−2i0000002i−2i2i−2i0000002-20000002i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ4622-2-22-20022i−2i2i−2i22-2-22-2-20002-2002i−2i0000002i−2i2i−2i0000002-20000002i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ4722-2-22-20022i−2i2i−2i22-2-22-2-2000-2200−2i2i0000002i−2i2i−2i000000-22000000−2i2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ4822-2-22-20022i−2i2i−2i22-2-22-2-2000-2200−2i2i0000002i−2i2i−2i000000-22000000−2i2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ4922-2-22-2002−2i2i−2i2i22-2-22-2-20002-200−2i2i000000−2i2i−2i2i0000002-2000000−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ5022-2-22-2002−2i2i−2i2i22-2-22-2-20002-200−2i2i000000−2i2i−2i2i0000002-2000000−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ5122-2-22-2002−2i2i−2i2i22-2-22-2-2000-22002i−2i000000−2i2i−2i2i000000-220000002i−2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ5222-2-22-2002−2i2i−2i2i22-2-22-2-2000-22002i−2i000000−2i2i−2i2i000000-220000002i−2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ5322-2-2-220022i−2i−2i2i-2-2222-2-202-20000002i−2i00002i−2i−2i2i00002-200000000002i−2i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ5422-2-2-220022i−2i−2i2i-2-2222-2-202-20000002i−2i00002i−2i−2i2i00002-200000000002i−2i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ5522-2-2-220022i−2i−2i2i-2-2222-2-20-22000000−2i2i00002i−2i−2i2i0000-220000000000−2i2i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ5622-2-2-220022i−2i−2i2i-2-2222-2-20-22000000−2i2i00002i−2i−2i2i0000-220000000000−2i2i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ5722-2-2-22002−2i2i2i−2i-2-2222-2-202-2000000−2i2i0000−2i2i2i−2i00002-20000000000−2i2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ5822-2-2-22002−2i2i2i−2i-2-2222-2-202-2000000−2i2i0000−2i2i2i−2i00002-20000000000−2i2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ5922-2-2-22002−2i2i2i−2i-2-2222-2-20-220000002i−2i0000−2i2i2i−2i0000-2200000000002i−2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ6022-2-2-22002−2i2i2i−2i-2-2222-2-20-220000002i−2i0000−2i2i2i−2i0000-2200000000002i−2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ614444-4-444-244-4-42222-2-2-2-400004-40000-2-222-2-22200000000-2200000000000000000000000000000000000000
χ624444-4-444-2-4-4442222-2-2-2-40000-440000-2-22222-2-2000000002-200000000000000000000000000000000000000
χ634444-4-4-4-4-244-4-42222-2-2-240000-44000022-2-2-2-222000000002-200000000000000000000000000000000000000
χ644444-4-4-4-4-2-4-4442222-2-2-2400004-4000022-2-222-2-200000000-2200000000000000000000000000000000000000
χ6544-4-44-400-24i−4i4i−4i-2-222-2220004-4004i−4i000000−2i2i−2i2i000000-22000000−2i2i00000000000000000000000000000000
χ6644-4-44-400-24i−4i4i−4i-2-222-222000-4400−4i4i000000−2i2i−2i2i0000002-20000002i−2i00000000000000000000000000000000
χ6744-4-44-400-2−4i4i−4i4i-2-222-2220004-400−4i4i0000002i−2i2i−2i000000-220000002i−2i00000000000000000000000000000000
χ6844-4-44-400-2−4i4i−4i4i-2-222-222000-44004i−4i0000002i−2i2i−2i0000002-2000000−2i2i00000000000000000000000000000000
χ6944-4-4-4400-24i−4i−4i4i22-2-2-22204-40000004i−4i0000−2i2i2i−2i0000-220000000000−2i2i000000000000000000000000000000
χ7044-4-4-4400-24i−4i−4i4i22-2-2-2220-44000000−4i4i0000−2i2i2i−2i00002-200000000002i−2i000000000000000000000000000000
χ7144-4-4-4400-2−4i4i4i−4i22-2-2-22204-4000000−4i4i00002i−2i−2i2i0000-2200000000002i−2i000000000000000000000000000000
χ7244-4-4-4400-2−4i4i4i−4i22-2-2-2220-440000004i−4i00002i−2i−2i2i00002-20000000000−2i2i000000000000000000000000000000
χ734-44-4004-4400000000-44-4000000000004-40000002i−2i2i−2i0000002i−2i2i−2i00002i−2i2i−2i00000000000000000000000000
χ744-44-4004-4400000000-44-4000000000004-4000000−2i2i−2i2i000000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000000000
χ754-44-4004-4-20000−2i32i3−2i32i32-2200000000000-22−2i32i300002i−2i2i−2i0000002ζ7−2ζ72ζ11−2ζ1100002ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ764-44-4004-4-20000−2i32i3−2i32i32-2200000000000-22−2i32i30000−2i2i−2i2i000000−2ζ72ζ7−2ζ112ζ110000−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ774-44-4004-4-200002i3−2i32i3−2i32-2200000000000-222i3−2i300002i−2i2i−2i0000002ζ11−2ζ112ζ7−2ζ700002ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ784-44-4004-4-200002i3−2i32i3−2i32-2200000000000-222i3−2i30000−2i2i−2i2i000000−2ζ112ζ11−2ζ72ζ70000−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ794-44-400-44400000000-44-400000000000-440000002i−2i−2i2i0000002i−2i2i−2i0000−2i2i−2i2i00000000000000000000000000
χ804-44-400-44400000000-44-400000000000-44000000−2i2i2i−2i000000−2i2i−2i2i00002i−2i2i−2i00000000000000000000000000
χ814-44-400-44-20000−2i32i3−2i32i32-22000000000002-22i3−2i300002i−2i−2i2i0000002ζ7−2ζ72ζ11−2ζ110000−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ824-44-400-44-20000−2i32i3−2i32i32-22000000000002-22i3−2i30000−2i2i2i−2i000000−2ζ72ζ7−2ζ112ζ1100002ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ834-44-400-44-200002i3−2i32i3−2i32-22000000000002-2−2i32i300002i−2i−2i2i0000002ζ11−2ζ112ζ7−2ζ70000−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ844-44-400-44-200002i3−2i32i3−2i32-22000000000002-2−2i32i30000−2i2i2i−2i000000−2ζ112ζ11−2ζ72ζ700002ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ858-8-880000800000000-8-880000000000000000000000000000000000000000000000000000000000000000000
χ868-8-880000-40000−4i34i34i3−4i344-40000000000000000000000000000000000000000000000000000000000000000000
χ878-8-880000-400004i3−4i3−4i34i344-40000000000000000000000000000000000000000000000000000000000000000000

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