Finite Group Databasebeta

← Group #10945068

Character table — Group #10945068

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order122222222234466666662222444444466661212121222446666666612121212121212121212444444444444444444121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111
χ811111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1
χ911111111111-1-1111111111-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-11-111-1-11-11-1
χ1011111111111-1-1111111111-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1111-111-1-1-11-11
χ1111111111111-1-1111111111-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-1-111-1-111-1-111-1-1-11-1-111-11-11
χ1211111111111-1-1111111111-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-111-1-111-11-1-1111-11-1
χ1311111111111-1-11111111-1-111-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-11-1-1111-1-11
χ1411111111111-1-11111111-1-111-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-11-1-111-111-1
χ1511111111111-1-11111111-1-111-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-111-1-1-111-1
χ1611111111111-1-11111111-1-111-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-11-111-1-11-1-11
χ172222222222-122-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ182222222222-122-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-1-1-1-1-1-10000000000000000-2-211110000
χ192222222222-122-1-1-1-1-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-122221111-1-1-1-1-1-1-1-1-1-111110000000000000000-2-211110000
χ202222222222-122-1-1-1-1-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2111111111111-1-11111000000000000000022-1-1-1-10000
χ212222222222-1-2-2-1-1-1-1-1-1-122-2-2-2-2-222-2-2-1-1-1-1111122-2-2-1-111-1-1-1-1111111-1-11100000000000000002-2-1-1110000
χ222222222222-1-2-2-1-1-1-1-1-1-122-2-2-2-2-222-2-2-1-1-1-11111-2-222-1-1111111-1-1-1-111-1-1110000000000000000-2211-1-10000
χ232222222222-1-2-2-1-1-1-1-1-1-1-2-222-2-2-2-2-222-1-1-1-1111122-2-211-1-1-1-1-1-111111111-1-10000000000000000-2211-1-10000
χ242222222222-1-2-2-1-1-1-1-1-1-1-2-222-2-2-2-2-222-1-1-1-11111-2-22211-1-11111-1-1-1-11111-1-100000000000000002-2-1-1110000
χ25222222-2-2-2-2222222222222-2-22-2-2-2-222-2-2-2-22222000022-2-200000000-2-2-2-22200000000000000000000000000
χ26222222-2-2-2-22222222222-2-2222-2-222-2-2-2-2-2-222220000-2-22200000000-2-222-2-200000000000000000000000000
χ27222222-2-2-2-22-2-222222222222-222-2-2-2-2-2-2-2-2-2-2-2-2000022220000000022-2-2-2-200000000000000000000000000
χ28222222-2-2-2-22-2-22222222-2-2-2-2-2222222-2-2-2-2-2-2-2-20000-2-2-2-20000000022222200000000000000000000000000
χ29222222-2-2-2-2-122-1-1-1-1-1-1-122-2-22-2-2-2-2221111-1-1-1-10000-1-111−i3−i3i3i3−i3−i3i3i31111-1-1000000000000000000−i3i3−i3i30000
χ30222222-2-2-2-2-122-1-1-1-1-1-1-122-2-22-2-2-2-2221111-1-1-1-10000-1-111i3i3−i3−i3i3i3−i3−i31111-1-1000000000000000000i3−i3i3−i30000
χ31222222-2-2-2-2-122-1-1-1-1-1-1-1-2-2222-2-222-2-21111-1-1-1-1000011-1-1−i3−i3i3i3−i3−i3i3i311-1-111000000000000000000i3−i3i3−i30000
χ32222222-2-2-2-2-122-1-1-1-1-1-1-1-2-2222-2-222-2-21111-1-1-1-1000011-1-1i3i3−i3−i3i3i3−i3−i311-1-111000000000000000000−i3i3−i3i30000
χ33222222-2-2-2-2-1-2-2-1-1-1-1-1-1-12222-222-2-2-2-2111111110000-1-1-1-1−i3−i3i3i3i3i3−i3−i3-1-11111000000000000000000−i3i3i3−i30000
χ34222222-2-2-2-2-1-2-2-1-1-1-1-1-1-12222-222-2-2-2-2111111110000-1-1-1-1i3i3−i3−i3−i3−i3i3i3-1-11111000000000000000000i3−i3−i3i30000
χ35222222-2-2-2-2-1-2-2-1-1-1-1-1-1-1-2-2-2-2-22222221111111100001111−i3−i3i3i3i3i3−i3−i3-1-1-1-1-1-1000000000000000000i3−i3−i3i30000
χ36222222-2-2-2-2-1-2-2-1-1-1-1-1-1-1-2-2-2-2-22222221111111100001111i3i3−i3−i3−i3−i3i3i3-1-1-1-1-1-1000000000000000000−i3i3i3−i30000
χ372222-2-222-2-22222-2-2-2-2220000-22-2000022-2-222-2-200000000000000002-20000000022-2-20000-2-2220000000000
χ382222-2-222-2-22222-2-2-2-2220000-22-2000022-2-222-2-200000000000000002-200000000-2-222000022-2-20000000000
χ392222-2-222-2-22-2-22-2-2-2-22200002-22000022-2-2-2-2220000000000000000-220000000022220000-2-2-2-20000000000
χ402222-2-222-2-22-2-22-2-2-2-22200002-22000022-2-2-2-2220000000000000000-2200000000-2-2-2-2000022220000000000
χ412222-2-2-2-2222222-2-2-2-2220000-2-220000-2-22222-2-20000000000000000-22000022-2-20000-2-22200000000000000
χ422222-2-2-2-2222222-2-2-2-2220000-2-220000-2-22222-2-20000000000000000-220000-2-222000022-2-200000000000000
χ432222-2-2-2-2222-2-22-2-2-2-222000022-20000-2-222-2-22200000000000000002-2000022220000-2-2-2-200000000000000
χ442222-2-2-2-2222-2-22-2-2-2-222000022-20000-2-222-2-22200000000000000002-20000-2-2-2-20000222200000000000000
χ4522-2-22-22-22-2200-222-2-2-22002-2000002-22-22-200000000002-20000000000002-2002i−2i2i−2i00002i−2i2i−2i000000000000
χ4622-2-22-22-22-2200-222-2-2-22002-2000002-22-22-200000000002-20000000000002-200−2i2i−2i2i0000−2i2i−2i2i000000000000
χ4722-2-22-22-22-2200-222-2-2-2200-2200000-222-22-20000000000-22000000000000-22002i−2i−2i2i00002i−2i−2i2i000000000000
χ4822-2-22-22-22-2200-222-2-2-2200-2200000-222-22-20000000000-22000000000000-2200−2i2i2i−2i0000−2i2i2i−2i000000000000
χ4922-2-22-2-22-22200-222-2-2-22002-200000-22-22-2200000000002-2000000000000-222i−2i00002i−2i2i−2i00002i−2i0000000000
χ5022-2-22-2-22-22200-222-2-2-22002-200000-22-22-2200000000002-2000000000000-22−2i2i0000−2i2i−2i2i0000−2i2i0000000000
χ5122-2-22-2-22-22200-222-2-2-2200-22000002-2-22-220000000000-220000000000002-22i−2i0000−2i2i2i−2i0000−2i2i0000000000
χ5222-2-22-2-22-22200-222-2-2-2200-22000002-2-22-220000000000-220000000000002-2−2i2i00002i−2i−2i2i00002i−2i0000000000
χ5322-2-2-222-2-22200-2-2-222-222-2000002-2002-2-22000000002-20000000000002-2002i−2i002i−2i00−2i2i00−2i2i000000000000
χ5422-2-2-222-2-22200-2-2-222-222-2000002-2002-2-22000000002-20000000000002-200−2i2i00−2i2i002i−2i002i−2i000000000000
χ5522-2-2-222-2-22200-2-2-222-22-2200000-22002-2-2200000000-22000000000000-22002i−2i00−2i2i00−2i2i002i−2i000000000000
χ5622-2-2-222-2-22200-2-2-222-22-2200000-22002-2-2200000000-22000000000000-2200−2i2i002i−2i002i−2i00−2i2i000000000000
χ5722-2-2-22-222-2200-2-2-222-222-200000-2200-222-2000000002-2000000000000-2200002i−2i00−2i2i00−2i2i002i−2i0000000000
χ5822-2-2-22-222-2200-2-2-222-222-200000-2200-222-2000000002-2000000000000-220000−2i2i002i−2i002i−2i00−2i2i0000000000
χ5922-2-2-22-222-2200-2-2-222-22-22000002-200-222-200000000-220000000000002-200002i−2i002i−2i00−2i2i00−2i2i0000000000
χ6022-2-2-22-222-2200-2-2-222-22-22000002-200-222-200000000-220000000000002-20000−2i2i00−2i2i002i−2i002i−2i0000000000
χ614444-4-444-4-4-244-22222-2-20000-44-40000-2-222-2-2220000000000000000-22000000000000000000000000000000
χ624444-4-444-4-4-2-4-4-22222-2-200004-440000-2-22222-2-200000000000000002-2000000000000000000000000000000
χ634444-4-4-4-444-244-22222-2-20000-4-44000022-2-2-2-22200000000000000002-2000000000000000000000000000000
χ644444-4-4-4-444-2-4-4-22222-2-2000044-4000022-2-222-2-20000000000000000-22000000000000000000000000000000
χ6544-4-44-44-44-4-2002-2-2222-2004-4000004-4-22-220000000000-22000000000000-2200000000000000000000000000
χ6644-4-44-44-44-4-2002-2-2222-200-4400000-44-22-2200000000002-20000000000002-200000000000000000000000000
χ6744-4-44-4-44-44-2002-2-2222-2004-400000-442-22-20000000000-220000000000002-200000000000000000000000000
χ6844-4-44-4-44-44-2002-2-2222-200-44000004-42-22-200000000002-2000000000000-2200000000000000000000000000
χ6944-4-4-444-4-44-200222-2-22-24-4000004-400-222-200000000-22000000000000-220000000000000000000000000000
χ7044-4-4-444-4-44-200222-2-22-2-4400000-4400-222-2000000002-20000000000002-20000000000000000000000000000
χ7144-4-4-44-444-4-200222-2-22-24-400000-44002-2-2200000000-220000000000002-20000000000000000000000000000
χ7244-4-4-44-444-4-200222-2-22-2-44000004-4002-2-22000000002-2000000000000-220000000000000000000000000000
χ734-44-400000044i−4i40000-4-40000000000000004i−4i002-22i−2i00002-22-22i−2i2i−2i00000000000000000000000000000000
χ744-44-400000044i−4i40000-4-40000000000000004i−4i00-22−2i2i0000-22-22−2i2i−2i2i00000000000000000000000000000000
χ754-44-40000004−4i4i40000-4-4000000000000000−4i4i002-2−2i2i00002-22-2−2i2i−2i2i00000000000000000000000000000000
χ764-44-40000004−4i4i40000-4-4000000000000000−4i4i00-222i−2i0000-22-222i−2i2i−2i00000000000000000000000000000000
χ774-44-4000000-24i−4i-2−2i32i3−2i32i322000000000000000−2i2i23−232-22i−2i0000−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ700000000000000000000000000000000
χ784-44-4000000-24i−4i-2−2i32i3−2i32i322000000000000000−2i2i23−23-22−2i2i00001+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ700000000000000000000000000000000
χ794-44-4000000-24i−4i-22i3−2i32i3−2i322000000000000000−2i2i−23232-22i−2i0000−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ1100000000000000000000000000000000
χ804-44-4000000-24i−4i-22i3−2i32i3−2i322000000000000000−2i2i−2323-22−2i2i00001−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ1100000000000000000000000000000000
χ814-44-4000000-2−4i4i-2−2i32i3−2i32i3220000000000000002i−2i−23232-2−2i2i0000−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ700000000000000000000000000000000
χ824-44-4000000-2−4i4i-2−2i32i3−2i32i3220000000000000002i−2i−2323-222i−2i00001+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ700000000000000000000000000000000
χ834-44-4000000-2−4i4i-22i3−2i32i3−2i3220000000000000002i−2i23−232-2−2i2i0000−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ1100000000000000000000000000000000
χ844-44-4000000-2−4i4i-22i3−2i32i3−2i3220000000000000002i−2i23−23-222i−2i00001−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ1100000000000000000000000000000000
χ858-8-88000000800-800008-80000000000000000000000000000000000000000000000000000000000000000000
χ868-8-88000000-4004−4i34i34i3−4i3-440000000000000000000000000000000000000000000000000000000000000000000
χ878-8-88000000-40044i3−4i3−4i34i3-440000000000000000000000000000000000000000000000000000000000000000000

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